Show Working

Geometry and measuresFoundation and Higher

Congruent triangles GCSE questions with answers

6 congruent triangles questions to try, each with the answer and the full working one tap away. Every question here was made and worked out by the Show Working maths engine, not typed in by hand.

Congruent triangles are exactly the same shape and size. Questions show two triangles and ask which condition proves they are congruent: SSS, SAS, ASA or RHS.

Quiz yourself: 6 questions

Worked example 1: congruent triangles

The two triangles are congruent. Which condition proves it?
A: SSS
B: SAS
C: ASA
D: RHS

7 cm6 cm8 cm7 cm6 cm8 cm
Not drawn accurately
  1. SSS: three sides. SAS: two sides and the angle between them. ASA: two angles and the side between them. RHS: a right angle, the hypotenuse and one other side.
  2. Here all three sides are equal, so the condition is SSS.
  3. So the answer is A.

Answer A

01 / Quiz yourselfTry it, then tap to check

Congruent triangles questions to try

Work each one out on paper first. Then open the answer and compare your working with ours, step by step.

01 / Congruent trianglesBoth tiers

The two triangles are congruent. Which condition proves it?
A: SSS
B: SAS
C: ASA
D: RHS

10 cm7 cm8 cm10 cm7 cm8 cm
Not drawn accurately
Show the answer and working
  1. SSS: three sides. SAS: two sides and the angle between them. ASA: two angles and the side between them. RHS: a right angle, the hypotenuse and one other side.
  2. Here all three sides are equal, so the condition is SSS.
  3. So the answer is A.

Answer A

02 / Congruent trianglesBoth tiers

The two triangles are congruent. Which condition proves it?
A: SSS
B: SAS
C: ASA
D: RHS

11 cm39°55°11 cm39°55°
Not drawn accurately
Show the answer and working
  1. SSS: three sides. SAS: two sides and the angle between them. ASA: two angles and the side between them. RHS: a right angle, the hypotenuse and one other side.
  2. Here two angles and the side between them are equal, so the condition is ASA.
  3. So the answer is C.

Answer C

03 / Congruent trianglesBoth tiers

The two triangles are congruent. Which condition proves it?
A: SSS
B: SAS
C: ASA
D: RHS

7 cm56°88°7 cm56°88°
Not drawn accurately
Show the answer and working
  1. SSS: three sides. SAS: two sides and the angle between them. ASA: two angles and the side between them. RHS: a right angle, the hypotenuse and one other side.
  2. Here two angles and the side between them are equal, so the condition is ASA.
  3. So the answer is C.

Answer C

04 / Congruent trianglesBoth tiers

The two triangles are congruent. Which condition proves it?
A: SSS
B: SAS
C: ASA
D: RHS

8 cm5 cm7 cm8 cm5 cm7 cm
Not drawn accurately
Show the answer and working
  1. SSS: three sides. SAS: two sides and the angle between them. ASA: two angles and the side between them. RHS: a right angle, the hypotenuse and one other side.
  2. Here all three sides are equal, so the condition is SSS.
  3. So the answer is A.

Answer A

05 / Congruent trianglesBoth tiers

The two triangles are congruent. Which condition proves it?
A: SSS
B: SAS
C: ASA
D: RHS

7 cm8 cm6 cm7 cm8 cm6 cm
Not drawn accurately
Show the answer and working
  1. SSS: three sides. SAS: two sides and the angle between them. ASA: two angles and the side between them. RHS: a right angle, the hypotenuse and one other side.
  2. Here all three sides are equal, so the condition is SSS.
  3. So the answer is A.

Answer A

06 / Congruent trianglesBoth tiers

The two triangles are congruent. Which condition proves it?
A: SSS
B: SAS
C: ASA
D: RHS

9 cm6 cm8 cm9 cm6 cm8 cm
Not drawn accurately
Show the answer and working
  1. SSS: three sides. SAS: two sides and the angle between them. ASA: two angles and the side between them. RHS: a right angle, the hypotenuse and one other side.
  2. Here all three sides are equal, so the condition is SSS.
  3. So the answer is A.

Answer A

02 / What's covered1 kind of question

Congruent triangles at GCSE and where marks go

  • Congruent trianglesBoth tiers

Worked example 2: congruent triangles

The two triangles are congruent. Which condition proves it?
A: SSS
B: SAS
C: ASA
D: RHS

8 cm6 cm39°8 cm6 cm39°
Not drawn accurately
  1. SSS: three sides. SAS: two sides and the angle between them. ASA: two angles and the side between them. RHS: a right angle, the hypotenuse and one other side.
  2. Here two sides and the angle between them are equal, so the condition is SAS.
  3. So the answer is B.

Answer B

A common mistake

Thinking three equal angles prove two triangles are congruent. Equal angles only show they are the same shape. One could be bigger than the other, so they are similar but not always congruent.

03 / Practise itiPhone and iPad

More congruent triangles questions in Show Working

In the app, Congruent triangles makes fresh questions every time, so they never run out. Tap Show me one to see a new worked example straight away, or practise ten and open the working whenever you are stuck. Forgotten a method? Type it into Look up and the answer is there.

Coming soon to the App Store

More geometry and measures topics

Angles and bearingsArea and perimeterCirclesVolume and surface areaPythagorasTrigonometryConverting unitsSimilar shapesSine and cosine rulesCircle theoremsVectorsTransformationsAll GCSE maths topics
The worked answer in Show Working: the answer, then numbered steps in plain words

Show WorkingComing soon to the App Store