Two triangles are congruent if they have the same shape and size. There are four conditions to show two triangles are congruent: 1) three equal sides (SSS), 2) two equal sides and the included angle (SAS), 3) two equal angles and the side between them (ASA), 4) a right angle, equal hypotenuse, and one other equal side (RHS). Once congruence is shown, the corresponding parts of the triangles are equal.

1. Unit 8: Transformations
GCSE Higher Tier 1

2. I can solve complex GCSE style
questions on congruency.
I understand what ‘congruency’
means.
I can show that two triangles are
congruent.
STARTER:
Which of these shapes is NOT congruent to the others?
8.1 – Congruent Triangles.
Keywords:
Congruency
Triangles
a) b) c) d)

3. Two shapes are congruent if they are exactly the same size and shape.
For example, these triangles are all congruent.
Notice that the triangles can be differently oriented (reflected or rotated).

4. Any one of the following four conditions is sufficient for two triangles to be congruent.
Condition 1:
‘All three sides of one triangle are equal to the corresponding sides of the other
triangle.’
2.4cm 2.2cm
3cm
3cm
2.4cm
2.2cm
This condition is known as SSS (side, side, side).

5. Any one of the following four conditions is sufficient for two triangles to be congruent.
Condition 2:
‘Two sides and the angle between them of one triangle are equal to the
corresponding sides and angle of the other triangle.’
This condition is known as SAS (side, angle, side).
4cm 3cm 3cm
4cm
50°
50°

6. Any one of the following four conditions is sufficient for two triangles to be congruent.
Condition 3:
‘Two angles and the side between of one triangle are equal to the corresponding
angles and sides of the other triangle.’
This condition is known as ASA (angle, side, angle).
4cm
4cm
30°
75°
75° 30°

7. Any one of the following four conditions is sufficient for two triangles to be congruent.
Condition 4:
‘Both triangles have a right angle, an equal hypotenuse and another equal side.’
This condition is known as RHS (right angle, hypotenuse, side).
4cm
9cm
4cm
9cm

8. Once you have shown that triangle ABC is congruent to triangle PQR by
one of the above conditions, it means that:
A = P AB = PQ
B = Q BC = QR
C = R AC = PR
In other words, the points ABC correspond exactly to the points PQR in
that order. Triangle ABC is congruent to PQR can be written as ΔABC ≡
ΔPQR.
A
B
C
P
R
Q

9. ABCD is a kite. Prove that triangle ABC is congruent to triangle ADC.
Grade B Grade B
5cm
12cm 12cm
5cm
A
B
C
D
AB = AD
BC = CD
AC is common.
So: ΔABC = ΔADC (SSS)

10. Grade B
Grade B
The triangles in each pair are congruent. State the condition that shows that
the triangles are congruent.
5cm
3cm
75° 3cm
5cm
7cm
4cm 7cm
4cm
7cm
5cm 8cm
35° 70° 35°
a) b)
c) d)

11. Grade A
Grade A
Draw a rectangle EFGH. Draw in the
diagonal EG. Prove that triangle EFG
is congruent to triangle EHG.
Draw an isosceles triangle ABC
where AB = AC. Draw the line from
A to X, the midpoint of BC. Prove
that triangle ABX is congruent to
triangle ACX.
In the diagram
ABCD and DEFG
are squares. Use
congruent triangles
to prove that AE =
CG.
Jez says that these two triangles
are congruent because of ASA.
Explain why he is wrong.
3cm
42° 35°
3cm
42° 35°

12. LO: I understand what ‘congruency’ means. (Bc)
I can show that two triangles are congruent. (Bb)
I can solve GCSE style questions involving congruent triangles. (Ac)