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Junior Cycle · Junior Cycle Maths

Junior Cycle Maths: Congruent & similar triangles

How often Congruent & similar triangles comes up on the Maths papers, every year it was asked, and questions to try.

HL Asked on 3 of the last 5 Higher Level papers, most recently in 2025. most years

OL Asked on 1 of the last 5 Ordinary Level papers, most recently in 2022.

Congruent & similar triangles, Higher Level(7 marks)

Quick ones on Congruent & similar triangles.

(a)Which of these is NOT a test for congruent triangles?
  1. SAS
  2. AAA
  3. RHS
(b)Two triangles are similar with scale factor 3. A 4 cm side in the smaller one matches what length?
  1. 1.33 cm
  2. 7 cm
  3. 12 cm
(c)Two triangles are similar: a 4 cm side matches a 10 cm side. What does a 6 cm side in the small triangle match?
  1. 15 cm
  2. 2.4 cm
  3. 12 cm
Show the answers

(a) AAA

(b) 12 cm

(c) 15 cm

Your turn: Higher Level questions on Congruent & similar triangles.

Higher Level

Asked on 3 of the last 5 Higher Level papers, most recently in 2025. most years

Every paper, year by year

YearWhere it came up
2026Not asked
2025Q6
2024Q13
2023Q14
2022Not asked

Links open the State Examinations Commission’s paper for that year.

More Congruent & similar triangles questions

Congruent & similar triangles, 2 marks

In triangle ABC, a line parallel to BC cuts [AB] in the ratio 2 : 3. In what ratio does it cut [AC]?

  1. 3 : 2
  2. 2 : 5
  3. 2 : 3
Show the answer

2 : 3

A line parallel to one side of a triangle cuts the other two sides in the same ratio (theorem 12). So [AC] is also cut 2 : 3, measured from A.

Congruent & similar triangles, 3 marks

DE ∥ BC, with D on [AB] and E on [AC]. |AD| = 4, |DB| = 6 and |AE| = 5. Find |EC|.

  1. 3.3
  2. 7.5
  3. 7
Show the answer

7.5

The parallel line cuts both sides in the same ratio: |AD| : |DB| = |AE| : |EC|, so 4/6 = 5/|EC| and |EC| = 5 × 6 ÷ 4 = 7.5.

Ordinary Level

Asked on 1 of the last 5 Ordinary Level papers, most recently in 2022.

Every paper, year by year

YearWhere it came up
2026Not asked
2025Not asked
2024Not asked
2023Not asked
2022Q7

Links open the State Examinations Commission’s paper for that year.

More Congruent & similar triangles questions

Congruent & similar triangles, 2 marks

Two triangles are congruent. What does this mean?

  1. Same shape, different size
  2. Same area, different shape
  3. Same shape and same size
Show the answer

Same shape and same size

Congruent triangles are exact copies: all three sides and all three angles match. Same shape but a different size is similar, not congruent.

Congruent & similar triangles, 2 marks

Two triangles have all three pairs of sides equal. Which test proves they are congruent?

  1. ASA
  2. SSS
  3. SAS
Show the answer

SSS

SSS means side, side, side. If all three pairs of sides are equal, the triangles must be congruent. SAS and ASA need an angle.

Congruent & similar triangles, 3 marks

Two triangles are similar. The small one has sides 3, 4 and 5 cm. The big one's shortest side is 6 cm. Find its longest side.

  1. 10 cm
  2. 8 cm
  3. 15 cm
Show the answer

10 cm

Similar triangles have their sides in the same ratio. 6 ÷ 3 = 2, so every side is doubled: 5 × 2 = 10 cm. Multiply, don't add.

Other Maths topics

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