AQA · Mathematics · 8300
GCSE Maths: Triangles: congruent
Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Triangles: congruent (Corbettmaths Video 328), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.
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What does it mean for two triangles to be congruent?
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They have exactly the same size and shape — corresponding sides and angles are equal.
The congruence condition ? means all three sides of one triangle equal the corresponding sides of another.
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SSS
The congruence condition ? means two sides and the included angle of one triangle equal the corresponding parts of another.
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SAS
The congruence condition ? means two angles and the included side of one triangle equal the corresponding parts of another.
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ASA
The congruence condition ? means a right angle, hypotenuse, and one other side of one triangle equal the corresponding parts of another.
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RHS
Can AAA (three angles) be used to prove two triangles are congruent?
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No. AAA proves triangles are similar (same shape), not congruent (same size and shape). Triangles can have the same angles but different sizes.
Are two triangles with one side of 10 cm, one angle of 45°, and one angle of 85° necessarily congruent?
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No. Without knowing where the side is relative to the angles (e.g., whether it's the included side), we cannot determine congruence.
Are two triangles with sides 3 cm, 9 cm, and 10 cm necessarily congruent?
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Yes. All three sides match (SSS condition), so the triangles must be congruent.
In SAS congruence, why must the angle be the included angle between the two sides?
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If the angle is not between the two given sides, the triangles may not be congruent — the configuration matters for determining shape uniquely.
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