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Congruent triangles
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EasyQuestion 1
[2 marks]State which congruence condition (SSS, SAS, ASA, or RHS) applies:
Triangle ABC has AB = 5 cm, BC = 7 cm, angle ABC = 60°.
Triangle DEF has DE = 5 cm, EF = 7 cm, angle DEF = 60°.
Solution for Question 1
MediumQuestion 2
[3 marks]ABCD is a parallelogram. Prove that triangles ABC and CDA are congruent.
Solution for Question 2
HardQuestion 3
[4 marks]In the diagram, AB = AC and M is the midpoint of BC.
Prove that triangles ABM and ACM are congruent, and hence prove that angle AMB = 90°.
Solution for Question 3
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Generate Unlimited QuestionsAbout Congruent triangles in AQA GCSE
Congruent shapes are identical - same size and shape. Two triangles are congruent if they satisfy one of four conditions: SSS (three sides equal), SAS (two sides and the included angle), ASA or AAS (two angles and a corresponding side), or RHS (right angle, hypotenuse, and one other side).
To prove congruence, identify which condition applies and show all the necessary measurements match. Be careful with SAS - the angle must be between the two sides. ASA and AAS are effectively the same since the third angle is determined by the other two.
In proof questions, clearly state the condition you're using and list the equal measurements systematically.
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