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Congruent triangles practice questions with answers

Higher · Grade 7 · Non-calculator

A second set of congruent triangles questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

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Question 1 Easy

A triangle has two angles and the included side. Name the condition.

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Answer: ASA

  1. The side connects the two known angles.
  2. Criterion is ASA.
  • Method (1): The side connects the two known angles.
  • Accuracy (1): Criterion is ASA.

Question 2 Easy

A triangle has all three sides known. Name the condition.

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Answer: SSS

  1. Three corresponding sides are equal.
  2. Criterion is SSS.
  • Method (1): Three corresponding sides are equal.
  • Accuracy (1): Criterion is SSS.

Question 3 Medium

A roof truss triangle has two angles and the included side known. Name the condition.

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Answer: ASA

  1. Side lies directly between the two angles.
  2. Criterion is ASA.
  • Method (1): Side lies directly between the two angles.
  • Accuracy (1): Criterion is ASA.

Question 4 Medium

Triangle ABC is congruent to triangle DEF. If AB = 8 cm, what is the length of DE?

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Answer: 8

  1. Corresponding sides of congruent triangles are equal.
  2. DE = AB = 8 cm.
  • Method (1): Corresponding sides of congruent triangles are equal.
  • Accuracy (1): DE = AB = 8 cm.

Question 5 Hard

A kite triangle has two sides and the included angle known. Name the condition.

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Answer: SAS

  1. Two adjacent sides and their included angle match.
  2. Criterion is SAS.
  • Method (1): Two adjacent sides and their included angle match.
  • Accuracy (1): Criterion is SAS.

Question 6 Hard

A bracket has all three sides known. Name the condition.

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Answer: SSS

  1. Three known side lengths fix the shape.
  2. Criterion is SSS.
  • Method (1): Three known side lengths fix the shape.
  • Accuracy (1): Criterion is SSS.

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 12 marks

Triangles ABC and PQR have angle A = angle P, angle B = angle Q and BC = QR. Name the condition that shows the triangles are congruent.

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Answer: AAS

  1. Two angles are equal, and the equal side BC is not between angles A and B.
  2. Two angles and a non-included side give the condition AAS.
  • Method (1): Two angles and a side, with the side not between the angles
  • Accuracy (1): AAS

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

What does the congruence condition SAS stand for?

  1. two sides and the included angle
  2. two angles and the included side
  3. three sides
  4. right angle and hypotenuse
Show answer

two sides and the included angle SAS stands for Side-Angle-Side (included angle).

Check 2

What does the congruence condition ASA stand for?

  1. two angles and the included side
  2. two sides and the included angle
  3. two angles and a non-included side
  4. all three angles
Show answer

two angles and the included side ASA stands for Angle-Side-Angle (included side).

Check 3

What does the congruence condition AAS stand for?

  1. two angles and a side that is not between them
  2. two angles and the included side
  3. two sides and an angle
  4. three angles
Show answer

two angles and a side that is not between them AAS uses two angles and a non-included side.

Check 4

Why is AAS a valid congruence condition even if the side is not included?

  1. the third angle is fixed because angles in a triangle sum to 180°
  2. all triangles are similar
  3. the hypotenuse is always known
  4. angles do not affect side lengths
Show answer

the third angle is fixed because angles in a triangle sum to 180° Knowing two angles determines the third angle (180° sum).

Check 5

What does the congruence condition SSS stand for?

  1. all three sides equal
  2. two sides and one angle
  3. three equal angles
  4. side scale factor
Show answer

all three sides equal SSS stands for Side-Side-Side.

Check 6

What does the congruence condition RHS stand for?

  1. Right angle, Hypotenuse and another Side
  2. Radius, Height and Side
  3. Ratio, Hypotenuse and Scale
  4. Right angle, Horizontal and Slope
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Right angle, Hypotenuse and another Side RHS requires a Right angle, Hypotenuse and one other Side.

Check 7

What does the word "included" mean in SAS and ASA?

  1. situated directly between the other two given elements
  2. outside the triangle
  3. adjacent to the hypotenuse
  4. opposite the longest side
Show answer

situated directly between the other two given elements An included angle is between two sides; an included side is between two angles.

Check 8

Why is AAA not a condition for congruence?

  1. it only proves triangles are similar (same shape, possibly different sizes)
  2. triangles cannot have three equal angles
  3. it proves congruence only for right triangles
  4. angles do not determine shape
Show answer

it only proves triangles are similar (same shape, possibly different sizes) Triangles with equal angles can be enlargements of each other.

Check 9

Which congruence condition requires the hypotenuse of a right-angled triangle?

  1. RHS
  2. SAS
  3. ASA
  4. SSS
Show answer

RHS RHS explicitly requires the Hypotenuse.

Check 10

A student identifies two angles and a non-included side as ASA. What is the correct label?

  1. AAS
  2. SAS
  3. SSS
  4. RHS
Show answer

AAS A non-included side makes the condition AAS.

Check 11

If all three corresponding sides of two triangles are equal, which condition applies?

  1. SSS
  2. SAS
  3. ASA
  4. AAA
Show answer

SSS Three equal sides establish SSS congruence.

Check 12

Two sides and the angle between them match in two triangles. Which condition applies?

  1. SAS
  2. ASA
  3. AAS
  4. RHS
Show answer

SAS The angle is between the two sides, so SAS applies.

Check 13

Two angles and the side between them match in two triangles. Which condition applies?

  1. ASA
  2. AAS
  3. SAS
  4. SSS
Show answer

ASA The side is between the two angles, so ASA applies.

Check 14

Why is SSA (two sides and a non-included angle) not a valid congruence condition?

  1. it is ambiguous and can produce two different triangles
  2. it only works for equilateral triangles
  3. it always produces right angles
  4. three sides are always required
Show answer

it is ambiguous and can produce two different triangles SSA has the ambiguous case where two distinct triangles can share the measurements.

Check 15

Name the five valid conditions for proving two triangles congruent.

  1. SAS, ASA, AAS, SSS and RHS
  2. AAA, SAS, ASA, SSS and RHS
  3. SAS, ASA, AAS, SSA and SSS
  4. SSS, SAS, ASA, RHS and AAA
Show answer

SAS, ASA, AAS, SSS and RHS The five valid conditions are SAS, ASA, AAS, SSS and RHS.

Keep going with Congruent triangles

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