/maths/wjec/grade-7-7-14-congruent-triangles/questions","formulaUrl":null,"initialIndex":1,"initialQuestionWindow":[{"id":"d2ed8e4c-a3e3-40a7-a209-dc86a6c90efe","revisionId":"f95e200d-0b53-4c33-979b-c91496532f1a","questionNumber":"1","questionType":"LA","specification":"$$ABCD$ is a parallelogram\n\n![Diagram of a parallelogram ABCD.](https://assets.mathsgenie.co.uk/questions/08d3d73e-a0b6-40b4-a430-0b1d5cff247f.png)","difficulty":1,"difficultyBand":"medium","totalMarks":3,"sourceTitle":"Congruent Triangles","calculatorUse":"non_calc","parts":[{"id":"84b54223-116b-4a90-a16c-407b1de03ccc","label":"a","content":"Prove that triangle $ABC$ is congruent to triangle $BCD$.","markscheme":"- $AC = BD$ (opposite sides of a parallelogram are equal) M1\n- $AB = CD$ (opposite sides of a parallelogram are equal) M1\n- $BC$ is common to both triangles. Therefore, the triangles are congruent by SSS. A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"States $AC = BD$ with the reason that opposite sides of a parallelogram are equal.","code":"M"},{"id":"p2","marks":1,"description":"States $AB = CD$ with the reason that opposite sides of a parallelogram are equal.","code":"M"},{"id":"p3","marks":1,"description":"Identifies $BC$ as a common side and concludes congruence using SSS.","code":"A"}],"finalAnswers":[],"generatedAt":"2026-05-05T15:45:34.937Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"check_congruence_claim","label":"Use SSS congruence","steps":[{"type":"text","order":0,"title":"Match one side pair","content":"In the supplied diagram, $C$ is the lower-left vertex and $D$ is the lower-right vertex. Therefore, $AC$ and $BD$ are opposite sides of the parallelogram, so\n\n$$AC=BD$$\n\nStating this equality with the reason **opposite sides of a parallelogram are equal** earns the first **M1** mark.","highlights":[{"text":"$$ABCD$ is a parallelogram","location":"specification"}]},{"type":"text","order":1,"title":"Use the second pair","content":"The other pair of opposite sides is $AB$ and $CD$. Hence\n\n$$AB=CD$$\n\nAgain, the reason is that **opposite sides of a parallelogram are equal**. This earns the second **M1** mark.","highlights":[{"text":"$$ABCD$ is a parallelogram","location":"specification"}]},{"type":"text","order":2,"title":"Conclude using SSS","content":"The side $BC$ belongs to both triangles, so it is a **common side**:\n\n$$BC=BC$$\n\nAll three corresponding side pairs are equal, so the triangles are congruent by **SSS** (side-side-side). In correspondence order,\n\n$$\\triangle ABC\\cong\\triangle DCB$$\n\nThis proves that the triangles named in the question, $ABC$ and $BCD$, are congruent and earns the **A1** mark.","highlights":[{"text":"Prove that triangle $ABC$ is congruent to triangle $BCD$.","location":"specification"}]}]}],"generatedAt":"2026-07-19T07:17:24.833Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":16}},{"id":"0549a6d6-2086-4145-9e74-15b69724c571","revisionId":"1812fb96-da25-4794-86a8-37269e26c7e5","questionNumber":null,"questionType":"LA","specification":"$$PQRS$ is a parallelogram. $T$ is the point where the diagonals $PS$ and $QR$ meet.","difficulty":1,"difficultyBand":"medium","totalMarks":3,"sourceTitle":null,"calculatorUse":"non_calc","parts":[{"id":"080a22db-9024-44b3-a39c-f96b1d496552","label":"a","content":"Prove that triangle $PRT$ is congruent to triangle $QST$.","markscheme":"- $PR = QS$ (opposite sides of a parallelogram are equal) M1\n- $\\angle PRQ = \\angle SQR$ (alternate angles are equal) M1\n- $\\angle RPS = \\angle QSP$ (alternate angles are equal). Therefore, congruent by ASA. A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"States $PR = QS$ and provides the reason that opposite sides of a parallelogram are equal.","code":"M"},{"id":"p2","marks":1,"description":"Identifi

Congruent Triangles

Question 2

Congruent Triangles Questions

Congruent Triangles

Question 2

Congruent Triangles Questions