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All matching angles are equal
All matching lengths are multiplied by the same scale factor

","mcqOptions":[{"text":"

All matching angles are equal
All matching lengths are multiplied by the same scale factor

","correct":true,"explanation":"Similar shapes have identical corresponding angles and proportional corresponding lengths. A single linear scale factor must convert every matching length on one shape to the other."},{"text":"

All matching angles are multiplied by the same scale factor
All matching lengths are equal

","correct":false,"explanation":"Angles are not multiplied by the scale factor, and matching lengths need not be equal. Similar shapes have equal matching angles and matching lengths related by one scale factor."},{"text":"

All matching angles are equal
All matching areas are equal

","correct":false,"explanation":"Similar shapes can have different areas, so equal areas are not required. Their matching angles are equal, while every matching length is multiplied by the same scale factor."},{"text":"

All matching angles have the same total
All matching lengths differ by the same amount

","correct":false,"explanation":"Similarity requires individual matching angles to be equal, not merely equal angle totals. Matching lengths have a constant ratio rather than a constant difference."}]},{"id":"fba39530-53cf-6860-3507-c1ea839c22a6","cardType":"cloze","points":null,"front":"An enlargement means every length has been multiplied by one fixed number called the [ ].","back":"An enlargement means every length has been multiplied by one fixed number called the scale factor.","mcqOptions":[{"text":"scale factor","correct":true,"explanation":"The scale factor is the fixed multiplier applied to every length in an enlargement. Using one multiplier preserves the shape’s proportions and matching angles."},{"text":"area scale factor","correct":false,"explanation":"The area scale factor applies to areas and equals the square of the length scale factor. The fixed number multiplying every length is the scale factor."},{"text":"volume scale factor","correct":false,"explanation":"The volume scale factor describes how volumes change and equals the cube of the length scale factor. The multiplier applied directly to lengths is the scale factor."},{"text":"translation vector","correct":false,"explanation":"A translation vector specifies horizontal and vertical movement without changing size. The fixed multiplier used to enlarge every length is called the scale factor."}]},{"id":"8dfdb07b-0218-f4ad-0e77-4911c932602b","cardType":"basic","points":1,"front":"How do you identify corresponding sides in similar shapes?","back":"Match the vertices (corners) or find the sides between matching angle labels.","mcqOptions":[{"text":"Match the vertices (corners) or find the sides between matching angle labels.","correct":true,"explanation":"Corresponding vertices occupy equivalent positions in the similar shapes. Therefore, sides joining matching vertices, or lying between matching angle labels, are corresponding sides."},{"text":"Match the side lengths or find the sides in the same page position.","correct":false,"explanation":"Corresponding sides can have different lengths and positions because a similar shape may be enlarged, rotated or reflected. Match vertices or use the sides between matching angle labels."},{"text":"Match the parallel sides or find the sides with matching orientations.","correct":false,"explanation":"Rotation can change a side’s orientation, and corresponding sides need not appear parallel on the page. Match corresponding vertices or sides between matching angle labels instead."},{"text":"Match the longest sides or find the sides beside matching length labels.","correct":false,"explanation":"Matching longest sides can help, but it is not a complete method and length labels may differ after enlargement. Corresponding sides are identified using matching vertices or angles."}]},{"id":"c2cb661e-86a4-e018-6085-c5b0b5d2b2aa","cardType":"cloze","points":null,"front":"If triangle $ABC$ is similar to triangle $PQR$ and $AB$ matches $PQ$, the scale factor $k$ is calculated as $k = \\frac{\\text{[...]}}{AB}$.","back":"If triangle $ABC$ is similar to triangle $PQR$ and $AB$ matches $PQ$, the scale factor $k$ is calculated as $k = \\frac{\\boxed{PQ}}{AB}$.","mcqOptions":[{"text":"$$PQ$","correct":true,"explanation":"Since $AB$ corresponds to $PQ$, the scale factor from triangle $ABC$ to triangle $PQR$ is the new matching length $PQ$ divided by the original length $AB$."},{"text":"$$AC$","correct":false,"explanation":"This mixes two sides from triangle $ABC$ rather than comparing corresponding sides across the triangles. The numerator must be $PQ$, which corresponds directly to $AB$."},{"text":"$$QR$","correct":false,"explanation":"Although $QR$ belongs to triangle $PQR$, it does not correspond to $AB$. The numerator must be the matching side $PQ$ so the ratio compares equivalent lengths."},{"text":"$$PR$","correct":false,"explanation":"Using $PR$ pairs non-corresponding sides and therefore gives an invalid scale factor. Since $AB$ matches $PQ$, the required numerator is $PQ$."}]},{"id":"daa49b57-2a4a-5c98-fc77-7be70893313c","cardType":"cloze","points":null,"front":"If triangle $ABC$ is similar to triangle $PQR$ and $AB$ matches $PQ$, the scale factor $k$ is calculated as $k = \\frac{PQ}{\\text{[...]}}$.","back":"If triangle $ABC$ is similar to triangle $PQR$ and $AB$ matches $PQ$, the scale factor $k$ is calculated as $k = \\frac{PQ}{\\boxed{AB}}$.","mcqOptions":[{"text":"$$AB$","correct":true,"explanation":"The denominator is the original matching side $AB$. Dividing its corresponding new length $PQ$ by $AB$ gives the scale factor from triangle $ABC$ to triangle $PQR$."},{"text":"$$AC$","correct":false,"explanation":"This incorrectly pairs $PQ$ with a non-corresponding side. Since the question states that $AB$ matches $PQ$, the denominator must be $AB$."},{"text":"$$BC$","correct":false,"explanation":"Using $BC$ compares sides in different corresponding positions, so the ratio is not the required scale factor. The denominator must be $AB$, which matches $PQ$."},{"text":"$$QR$","correct":false,"explanation":"This compares two sides within triangle $PQR$ instead of corresponding sides from the two triangles. The correct denominator is $AB$, the side matching $PQ$."}]},{"id":"4b4eccb1-6133-223e-f99e-3cc949cae0f5","cardType":"basic","points":1,"front":"To find a missing length on a larger similar shape, what do you do with the scale factor?","back":"Multiply the corresponding length on the smaller shape by the scale factor.","mcqOptions":[{"text":"Multiply the corresponding length on the smaller shape by the scale factor.","correct":true,"explanation":"The scale factor from the smaller shape to the larger shape is greater than one. Multiplying a corresponding smaller length by it gives the larger length."},{"text":"Divide the corresponding length on the smaller shape by the scale factor.","correct":false,"explanation":"Dividing would make the smaller length even shorter, which reverses the required enlargement. Multiply the corresponding smaller length by the scale factor to obtain the larger length."},{"text":"Add the corresponding length on the smaller shape to the scale factor.","correct":false,"explanation":"A scale factor is a multiplier, not a fixed amount added to each side. Multiply the corresponding smaller length by the scale factor to preserve proportionality."},{"text":"Multiply the corresponding length on the smaller shape by the square of the scale factor.","correct":false,"explanation":"Squaring the scale factor is used when converting areas, not lengths. For a missing length, multiply the corresponding smaller length by the scale factor itself."}]},{"id":"249614bc-7564-3a4b-bfc2-4609ea28d1b3","cardType":"basic","points":1,"front":"To find a missing length on a smaller similar shape, what do you do with the scale factor?","back":"Divide the corresponding length on the larger shape by the scale factor.","mcqOptions":[{"text":"Divide the corresponding length on the larger shape by the scale factor.","correct":true,"explanation":"The scale factor multiplies smaller lengths to produce larger ones, so the inverse operation is required. Divide the corresponding larger length by the scale factor."},{"text":"Multiply the corresponding length on the larger shape by the scale factor.","correct":false,"explanation":"Multiplying would produce an even larger length rather than the required smaller one. Reverse the enlargement by dividing the corresponding larger length by the scale factor."},{"text":"Subtract the scale factor from the corresponding length on the larger shape.","correct":false,"explanation":"A scale factor describes a multiplicative relationship, not a fixed difference. Divide the corresponding larger length by the scale factor to find the smaller length."},{"text":"Divide the corresponding length on the larger shape by the square of the scale factor.","correct":false,"explanation":"Using the square confuses length scale factors with area scale factors and makes the result too small. Divide the larger length by the scale factor itself."}]},{"id":"cb19f7e4-b231-ccaa-eed4-e2ef3c45ec84","cardType":"basic","points":1,"front":"What is the relationship between a large triangle and a smaller triangle created by a line drawn parallel to one of its sides?","back":"The triangles are mathematically similar.","mcqOptions":[{"text":"The triangles are mathematically similar.","correct":true,"explanation":"The parallel line creates equal corresponding angles, while the triangles also share an angle. Equal matching angles establish that the two triangles are mathematically similar."},{"text":"The triangles are mathematically congruent.","correct":false,"explanation":"The triangles have equal corresponding angles but generally have different side lengths, so they are not congruent. The parallel line ensures that they are mathematically similar."},{"text":"The triangles have mathematically equal areas.","correct":false,"explanation":"The smaller triangle occupies only part of the larger triangle, so their areas are not equal. Parallel lines create equal matching angles, making the triangles mathematically similar."},{"text":"The triangles have mathematically equal perimeters.","correct":false,"explanation":"Similar triangles usually have perimeters related by the length scale factor rather than equal perimeters. The parallel line establishes equal matching angles, so the triangles are mathematically similar."}]},{"id":"ca2e537d-96b2-9171-aa48-33cad328f81f","cardType":"cloze","points":null,"front":"When a triangle side has been split by a parallel line, the full side length is found by adding the [ ] and the extra part together.","back":"When a triangle side has been split by a parallel line, the full side length is found by adding the small part and the extra part together.","mcqOptions":[{"text":"small part","correct":true,"explanation":"The full side is made from the small part plus the extra part, so these two adjacent lengths must be added together."},{"text":"whole side","correct":false,"explanation":"Adding the whole side to the extra part counts the extra section twice. The full length is found by adding the small part and the extra part."},{"text":"corresponding side","correct":false,"explanation":"A corresponding side belongs to the similar triangle comparison and is not necessarily a section of this side. Add the small part to the extra part."},{"text":"scale factor","correct":false,"explanation":"A scale factor is a multiplier, not a section with a length that can be added. The full side equals the small part plus the extra part."}]},{"id":"9be1ffbd-a382-bc57-1e4a-6ee4f16602dc","cardType":"cloze","points":null,"front":"When a triangle side has been split by a parallel line, the full side length is found by adding the small part and the [ ] together.","back":"When a triangle side has been split by a parallel line, the full side length is found by adding the small part and the extra part together.","mcqOptions":[{"text":"extra part","correct":true,"explanation":"The small part and the extra part are adjacent sections forming the complete side, so adding their lengths gives the full side length."},{"text":"whole length","correct":false,"explanation":"Adding the whole length to the small part counts that small section twice. The full side is formed by adding the small part and the extra part."},{"text":"parallel side","correct":false,"explanation":"The parallel side is a separate side of one of the similar triangles, not the missing section. Add the small part and the extra part."},{"text":"scale factor","correct":false,"explanation":"The scale factor compares corresponding lengths by multiplication or division; it is not a length section. The small part must be added to the extra part."}]},{"id":"cd0e95f6-1dd4-62b9-74a5-a8b1553f705f","cardType":"basic","points":2,"front":"In a \"bow-tie\" diagram with parallel sides, how are the corresponding sloping sides identified?","back":"They are the sides that lie on the same straight line passing through the crossing point.","mcqOptions":[{"text":"They are the sides that lie on the same straight line passing through the crossing point.","correct":true,"explanation":"Each pair of corresponding sloping sides forms one continuous straight line through the crossing point, allowing the sides in the two similar triangles to be matched."},{"text":"They are the sides that are parallel to each other on opposite sides of the crossing point.","correct":false,"explanation":"The sloping corresponding sides are not parallel; they continue along the same straight line through the crossing point. The other pair of sides is marked parallel."},{"text":"They are the sides that have the same measured length on either side of the crossing point.","correct":false,"explanation":"Corresponding sides of similar triangles need not have equal lengths unless the scale factor is 1. They are identified by lying on the same straight line."},{"text":"They are the sides that meet the same parallel side without passing through the crossing point.","correct":false,"explanation":"Matching sides by which parallel side they meet reverses the correspondence. Corresponding sloping sides lie on one straight line passing through the central crossing point."}]},{"id":"46e3e85c-15bd-ca69-7f4b-0c3e59c89379","cardType":"basic","points":1,"front":"How do you find the extra part (e.g., $ED$) of a side if you know the whole length ($AD$) and the small part ($AE$)?","back":"$$ED = AD - AE$ (Subtract the small part from the whole length).","mcqOptions":[{"text":"$$ED = AD - AE$ (Subtract the small part from the whole length).","correct":true,"explanation":"The whole side satisfies $AD = AE + ED$, so rearranging gives $ED = AD - AE$. The extra section is the whole minus the known small section."},{"text":"$$ED = AD + AE$ (Add the small part to the whole length).","correct":false,"explanation":"Adding $AE$ to the whole length counts the small section twice and produces a value larger than $AD$. The correct calculation is $ED = AD - AE$."},{"text":"$$ED = AE - AD$ (Subtract the whole length from the small part).","correct":false,"explanation":"This subtraction is reversed and would normally produce a negative length because $AD$ is the whole side. The correct order is $ED = AD - AE$."},{"text":"$$ED = AD \\div AE$ (Divide the whole length by the small part).","correct":false,"explanation":"Division finds a ratio or scale factor rather than the remaining length. Since $AD = AE + ED$, the extra part is found using $ED = AD - AE$."}]},{"id":"9c7601a3-5d51-1b14-314f-6a0a148e64a6","cardType":"basic","points":1,"front":"If the ratio of two corresponding sides $AB:AC$ is $2:5$, what scale factor takes $AB$ to $AC$?","back":"$$k = \\frac{5}{2}$ (or $2.5$)","mcqOptions":[{"text":"$$k = \\frac{5}{2}$ (or $2.5$)","correct":true,"explanation":"To map $AB$ to $AC$, divide the target length by the original length: $k = AC \\div AB = 5 \\div 2 = 2.5$."},{"text":"$$k = \\frac{2}{5}$ (or $0.4$)","correct":false,"explanation":"This reverses the scale factor and would map $AC$ back to $AB$. Taking $AB$ to $AC$ requires target divided by original, giving $\\frac{5}{2}$."},{"text":"$$k = \\frac{5}{3}$ (or $1.67$)","correct":false,"explanation":"Subtracting the ratio terms before dividing is not how scale factors are calculated. Divide the target value 5 by the original value 2 to obtain $\\frac{5}{2}$."},{"text":"$$k = \\frac{7}{2}$ (or $3.5$)","correct":false,"explanation":"Adding the ratio terms before dividing incorrectly changes the target length from 5 to 7. The required calculation is $5 \\div 2$, giving $\\frac{5}{2}$."}]},{"id":"1ecddd6b-c941-546b-ebc9-0664d29aab03","cardType":"cloze","points":null,"front":"If the ratio of corresponding lengths is $1:3$, the scale factor is [ ].","back":"If the ratio of corresponding lengths is $1:3$, the scale factor is 3.","mcqOptions":[{"text":"3","correct":true,"explanation":"The second corresponding length is three times the first because $3 \\div 1 = 3$. Therefore, the enlargement scale factor from the first shape to the second is 3."},{"text":"$$\\frac{1}{3}$","correct":false,"explanation":"This is the reciprocal scale factor and describes mapping the larger length back to the smaller one. From the first length to the second, the scale factor is 3."},{"text":"2","correct":false,"explanation":"Subtracting the ratio values gives the difference in ratio parts, not the scale factor. The multiplier from 1 part to 3 parts is $3 \\div 1 = 3$."},{"text":"4","correct":false,"explanation":"Adding the two ratio values does not give the enlargement multiplier. A length of 1 becomes 3, so the required scale factor is $3 \\div 1 = 3$."}]},{"id":"28977d6b-a2cf-5be2-6c07-b723ad9dc983","cardType":"basic","points":2,"front":"Why are two right-angled triangles similar if they share one other angle?","back":"Because they have two equal angles (the shared angle and the 90 degree angle), so the third must also be equal.","mcqOptions":[{"text":"Because they have two equal angles (the shared angle and the 90 degree angle), so the third must also be equal.","correct":true,"explanation":"Two pairs of corresponding angles are equal: the shared angle and the right angles. By angle-angle similarity, the triangles are similar, and their third angles also match."},{"text":"Because they have one equal angle (the shared angle), so all the remaining sides and angles must also be equal.","correct":false,"explanation":"One equal angle alone is insufficient to prove similarity. The proof works because both triangles also have a 90 degree angle, giving two equal corresponding angles."},{"text":"Because they have two equal sides (the sides beside the shared angle), so the third side must also be equal.","correct":false,"explanation":"Sharing an angle does not mean the adjacent sides have equal lengths. Similarity follows from two equal angles: the shared angle and the 90 degree angle."},{"text":"Because they have one right angle (the 90 degree angle), so every pair of right-angled triangles must be similar.","correct":false,"explanation":"A right angle alone does not establish similarity because right-angled triangles can have different acute angles. The additional shared angle supplies the second equal angle needed."}]},{"id":"4a14a5ed-bf13-85ce-5fa0-c0e8b4a0f576","cardType":"basic","points":2,"front":"How do you prove that two rectangles are not mathematically similar?","back":"Show that the length scale factor and the width scale factor are different.","mcqOptions":[{"text":"Show that the length scale factor and the width scale factor are different.","correct":true,"explanation":"Similar shapes require one constant scale factor for every pair of corresponding lengths. Different scale factors for the rectangles’ lengths and widths prove that they are not similar."},{"text":"Show that the length scale factor and the width scale factor are equal.","correct":false,"explanation":"Equal length and width scale factors support similarity rather than disprove it, because all corresponding sides change by the same multiplier. To prove non-similarity, show they differ."},{"text":"Show that the areas of the rectangles and the perimeters of the rectangles are different.","correct":false,"explanation":"Similar rectangles of different sizes normally have different areas and perimeters, so this does not disprove similarity. Instead, compare the length and width scale factors."},{"text":"Show that the corresponding angles and the right angles are equal.","correct":false,"explanation":"All rectangles have four equal 90 degree angles, including rectangles that are not similar. Non-similarity is proved when the length and width scale factors are different."}]},{"id":"4614b557-f7b4-f116-2f12-25d49fe492d8","cardType":"cloze","points":null,"front":"Even though all rectangles have equal angles (90 degrees), they are only similar if their matching sides have the [ ].","back":"Even though all rectangles have equal angles (90 degrees), they are only similar if their matching sides have the same multiplier.","mcqOptions":[{"text":"same multiplier","correct":true,"explanation":"Similar rectangles have one constant scale factor, so every pair of corresponding sides must be related by the same multiplier."},{"text":"same length","correct":false,"explanation":"Requiring equal side lengths would make the rectangles congruent, not merely similar. Similar rectangles can differ in size, provided corresponding sides have the same multiplier."},{"text":"same difference","correct":false,"explanation":"Similarity is based on multiplicative scaling, not adding or subtracting a constant difference. Corresponding sides must therefore have the same multiplier."},{"text":"same perimeter","correct":false,"explanation":"Equal perimeters do not guarantee that rectangles have matching proportions. For similarity, every pair of corresponding sides must have the same multiplier."}]},{"id":"8c63d428-26ab-7496-4f21-78cd991fc042","cardType":"basic","points":1,"front":"When performing a sanity check on a calculation, what should you observe about the larger triangle?","back":"Every corresponding length on the larger triangle must be larger by the same scale factor.","mcqOptions":[{"text":"Every corresponding length on the larger triangle must be larger by the same scale factor.","correct":true,"explanation":"Similarity applies one constant scale factor to all corresponding lengths, so every side of the larger triangle should increase by that same factor."},{"text":"Every corresponding length on the larger triangle must be larger by a different scale factor.","correct":false,"explanation":"Using different scale factors would change the triangle’s proportions, meaning the triangles were not similar. Every corresponding length must be enlarged by the same scale factor."},{"text":"Only one corresponding length on the larger triangle must be larger by the same scale factor.","correct":false,"explanation":"Checking only one pair of sides cannot confirm that the calculation preserves similarity. Every corresponding length must be larger by the same scale factor."},{"text":"Every corresponding length on the larger triangle must be larger by the same added amount.","correct":false,"explanation":"A common mistake is to add a fixed amount rather than multiply. Similar triangles require every corresponding length to be multiplied by the same scale factor."}]},{"id":"e1aaf6a1-2181-30dd-0f3b-391fad44044c","cardType":"basic","points":1,"front":"Which step should be taken before calculating values in a similarity diagram?","back":"Mark or label the corresponding sides on the diagram.","mcqOptions":[{"text":"Mark or label the corresponding sides on the diagram.","correct":true,"explanation":"Identifying corresponding sides first ensures that the correct lengths are compared and that the scale factor is applied in the correct direction."},{"text":"Add together all the known sides on the diagram.","correct":false,"explanation":"Adding known sides does not identify the matching measurements needed for similarity. First mark or label the corresponding sides on the diagram."},{"text":"Measure or estimate the unknown sides on the diagram.","correct":false,"explanation":"Similarity diagrams may not be drawn accurately, so measuring or estimating can mislead. First mark or label the corresponding sides before calculating."},{"text":"Multiply all of the labelled sides on the diagram.","correct":false,"explanation":"Multiplying every labelled side does not establish which lengths correspond or what scale factor to use. First mark or label the corresponding sides."}]},{"id":"b0864dbf-a887-576a-9a58-3e2c9a1c9f67","cardType":"cloze","points":null,"front":"Two shapes are mathematically similar if one is an [ ] of the other.","back":"Two shapes are mathematically similar if one is an enlargement of the other.","mcqOptions":[{"text":"enlargement","correct":true,"explanation":"An enlargement scales every length by one constant factor while preserving angles, so the original and resulting shapes are mathematically similar."},{"text":"distortion","correct":false,"explanation":"A distortion can alter angles or change different lengths by different factors, so it does not preserve similarity. The required transformation is an enlargement."},{"text":"shear","correct":false,"explanation":"A shear changes angles and therefore usually changes the shape’s proportions. Mathematically similar shapes are related by an enlargement."},{"text":"stretch","correct":false,"explanation":"A stretch may scale different directions by different amounts, changing the shape’s proportions. Similar shapes require a uniform enlargement with one scale factor."}]},{"id":"8390bd19-eb88-85df-8db2-3fb086bb35d0","cardType":"basic","points":1,"front":"If the parallel side on triangle A is 8cm and the matching side on triangle B is 20cm, what is the scale factor from A to B?","back":"$$2.5$ (calculated as $20 \\div 8$)","mcqOptions":[{"text":"$$2.5$ (calculated as $20 \\div 8$)","correct":true,"explanation":"The scale factor from A to B is the matching length in B divided by the matching length in A, giving $20 \\div 8 = 2.5$."},{"text":"$$0.4$ (calculated as $8 \\div 20$)","correct":false,"explanation":"This reverses the division and gives the scale factor from B to A. From A to B, calculate $20 \\div 8$, which equals $2.5$."},{"text":"$$12$ (calculated as $20 - 8$)","correct":false,"explanation":"Subtracting finds the difference between the lengths, not the multiplicative scale factor. Divide the B length by the A length: $20 \\div 8 = 2.5$."},{"text":"$$160$ (calculated as $20 \\times 8$)","correct":false,"explanation":"Multiplying the two matching lengths does not compare their sizes. The scale factor from A to B is $20 \\div 8 = 2.5$."}]},{"id":"277f8122-88cf-4122-04a0-af7f2dd79ea2","cardType":"basic","points":2,"front":"Outline the process for finding a missing length when only a ratio $AB:AC$ is given.","back":"

Convert the ratio into a scale factor fraction
Multiply the known length by that scale factor

","mcqOptions":[{"text":"

Convert the ratio into a scale factor fraction
Multiply the known length by that scale factor

","correct":true,"explanation":"The ratio establishes the multiplicative relationship between corresponding sides. Expressing it as a scale factor fraction and multiplying the known length gives the missing length."},{"text":"

Convert the ratio into a scale factor fraction
Add the known length to that scale factor

","correct":false,"explanation":"Adding the scale factor treats similarity as an additive relationship. After converting the ratio into a scale factor fraction, multiply the known length by it."},{"text":"

Convert the ratio into a length difference
Multiply the known length by that difference

","correct":false,"explanation":"A ratio describes multiplication, not a fixed difference between side lengths. Convert the ratio into a scale factor fraction, then multiply the known length by it."},{"text":"

Convert the known length into a scale factor fraction
Multiply the ratio by that scale factor

","correct":false,"explanation":"This swaps the roles of the ratio and the measured length. Convert the ratio into a scale factor fraction, then multiply the known length by that factor."}]}]}],"examCountdown":{"examDate":"2027-05-14","paperLabel":"Paper 1"},"heading":"Similar Shapes (Lengths)","title":"Similar Shapes (Lengths) Flashcards","topbar":{"backHref":"/gcse/maths/aqa/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"d1a083a2-5914-4e10-9582-9cfdf0da45ad","walled":"$L39"}],"$L3a","$L3b"]