Printable · GCSE Foundation · ages 14-16

Congruence criteria for triangles worksheet — GCSE Foundation

Fifteen questions on "congruence criteria for triangles" — DfE statement G5. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.

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Congruence criteria for triangles worksheet — GCSE Foundation

Maths · GCSE Foundation · G5 · Congruence criteria for triangles · 15 questions

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1.For two triangles to be proved congruent using SAS, which two facts must be true about both triangles?
(a)Two sides equal, with the angle between them equal
(b)Two angles equal, with the side between them equal
(c)All three pairs of sides equal
(d)Two sides equal, and any one angle equal
2.Two triangles are congruent to each other. What does this tell you about their angles and sides?
(a)All angles equal, sides may differ
(b)All sides equal, angles may differ
(c)Same area, angles and sides may differ
(d)All angles equal and all sides equal
3.Triangles PQS and RQS share the common side QS. PQ equals RQ, and PS equals RS. Which condition proves that triangle PQS is congruent to triangle RQS?
(a)Cannot prove — no angle given
(b)Only two pairs of sides — not enough
(c)SAS, using the angle at Q
(d)SSS, using shared side QS
4.Triangle ABC has AB = 6 cm, BC = 8 cm and angle B = 90°. Triangle XYZ has XY = 6 cm, YZ = 8 cm and angle Y = 90°. Which congruence statement correctly shows the matching vertices?
(a)ABC ≅ ZXY
(b)ABC ≅ ZYX
(c)ABC ≅ XYZ
(d)ABC ≅ YXZ
5.Triangle ABC has a right angle at B and hypotenuse AC = 17 cm, with AB = 8 cm. Triangle DEF has a right angle at E and hypotenuse DF = 17 cm. Which extra fact about DEF would complete the RHS condition for proving that ABC ≅ DEF, with the vertices matching in that order?
(a)Angle D = angle A
(b)BC = 8 cm
(c)EF = 8 cm
(d)DE = 8 cm
6.Triangle ABC has AB = 5 cm, BC = 7 cm and CA = 9 cm. Triangle DEF has DE = 5 cm, EF = 7 cm and FD = 9 cm. Which condition proves the two triangles are congruent?
(a)ASA - two angles and the included side equal
(b)SAS - two sides and the included angle equal
(c)RHS - right angle, hypotenuse and one side equal
(d)SSS - three sides equal
7.Triangle ABC has a right angle at B, hypotenuse AC = 13 cm and AB = 5 cm. Triangle DEF has a right angle at E, hypotenuse DF = 13 cm and DE = 5 cm. Which condition proves the two triangles are congruent?
(a)SSS - three sides equal
(b)RHS - right angle, hypotenuse and one side equal
(c)ASA - two angles and the included side equal
(d)SAS - two sides and the included angle equal
8.Triangles ABE and CDE share the vertex E, where lines AC and BD cross at E. AE equals CE, and BE equals DE. Angle AEB and angle CED are formed as vertically opposite angles where the lines cross. Which condition proves that triangle ABE is congruent to triangle CDE?
(a)ASA, vertically opposite angle at E
(b)Cannot prove — no angle measured
(c)SSS, three equal side pairs
(d)SAS, vertically opposite angle included
9.Triangle ABC has AB = 8 cm, angle B = 50° and BC = 6 cm. Triangle DEF has DE = 8 cm, angle E = 50° and EF = 6 cm. Which condition proves the two triangles are congruent?
(a)AAS - two angles and a non-included side equal
(b)SSS - three sides equal
(c)SAS - two sides and the included angle equal
(d)ASA - two angles and the included side equal
10.A sailmaker cuts two triangular sail panels from a pattern. Panel X has a 10 m side, with angles of 50° and 75° at its two ends. Panel Y also has a 10 m side, with angles of 50° and 75° at its two ends, in the same arrangement. The sailmaker wants to check the panels will match exactly, without cutting a third measurement. Which condition proves the two panels are congruent?
(a)SAS
(b)RHS
(c)ASA
(d)SSS
11.Triangle ABC has AB = 6 cm and BC = 9 cm, with angle A = 40°. Triangle DEF has DE = 6 cm and EF = 9 cm, with angle D = 40°. Meera says these facts prove the triangles are congruent by SAS. Is Meera correct?
(a)Yes — two sides and one angle match
(b)No — the angle given is not the included angle
(c)No — SSS needs three equal sides, not two
(d)Yes — SAS allows any equal angle, not just the included one
12.An isosceles triangle ABC has AB equal to AC. AM is a line from vertex A, perpendicular to BC, meeting BC at point M. Which condition proves that triangle ABM is congruent to triangle ACM?
(a)SAS, right angle as included angle
(b)ASA, AB as the included side
(c)SSS, using BM = CM as a fact
(d)RHS, using AM as common side
13.Triangle ABC has AB = (2x + 3) cm, BC = 11 cm and angle B = 90°. Triangle DEF has DE = 13 cm, EF = 11 cm and angle E = 90°. Given that the two triangles are congruent by SAS, work out the value of x.
(a)4
(b)10
(c)8
(d)5
14.Triangle ABC has AB = 10 cm, BC = 7 cm and angle A = 40°. Triangle DEF has DE = 10 cm, EF = 7 cm and angle D = 40°. Sam says the two triangles are congruent by SAS. Which statement about Sam's claim is correct?
(a)Wrong - none of the sides or angles match
(b)Correct, but by ASA rather than SAS
(c)Correct - two sides and an angle match
(d)Wrong - the given angle is not the included angle
15.Triangle ABC has AB = 5 cm and BC = 7 cm. Triangle DEF has DE = 5 cm and EF = 7 cm. Which extra fact would prove the triangles are congruent by SAS?
(a)angle C = angle F
(b)angle B = angle E
(c)AC = DF
(d)angle A = angle D

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