Congruence of Triangles — Practice

Question 1

Two triangles have sides 4 cm, 6 cm, 8 cm each. Which congruence criterion applies?

Accepted Answer

SSS criterion, since all three pairs of corresponding sides are equal.

Question 2

Triangle ABC has AB = 5 cm, angle A = 50, AC = 7 cm. Triangle PQR has PQ = 5 cm, angle P = 50, PR = 7 cm. Are they congruent? Which criterion?

Accepted Answer

Yes, by SAS: AB = PQ (side), angle A = angle P (included angle), AC = PR (side).

Question 3

In two right triangles, the hypotenuses are 13 cm and one side is 5 cm in each. Are they congruent?

Accepted Answer

Yes, by the RHS criterion (right angle, equal hypotenuse, and one equal side).

Question 4

Triangle ABC is congruent to triangle DEF. If angle A = 70 and angle B = 50, find angle F.

Accepted Answer

Angle C = 180 - (70 + 50) = 60. Since the triangles are congruent, angle F = angle C = 60 degrees.

Question 5

AB = CD and AB is parallel to CD, intersecting at O. Prove triangle AOB is congruent to triangle COD.

Accepted Answer

AB = CD (given). Angle OAB = angle OCD and angle OBA = angle ODC (alternate interior angles, AB parallel CD). So triangle AOB is congruent to triangle COD by ASA.

Practice — Congruence of Triangles

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