Question

Triangle ABC has been translated to create triangle A'B'C'. Angles C and C' are both 32 degrees, angles B and B' are both 72 degrees, and sides BC and B'C' are both 5 units long. Which postulate or theorem below would prove the two triangles are congruent?

Answer 1

Δ ABC and Δ A'B'C' are congruent.

Proof: BC = B'C' = 5 units (given)

Angle B = Angle B' = 72° (given)
Angle C = Angle C' = 32° (given)

The 2 tringles are ten equal ASA

Answer 2

ΔABC ≅ ΔA'B'C' are congruent by ASA postulate

Explanation:

Let's draw ΔABC and ΔA'B'C'

Statement Reason

i) ∠C = ∠C' = 32° Given

ii) ∠B = ∠B' = 72° Given

iii) BC = B'C' = 5 Given

IV) ΔABC ≅ ΔA'B'C' If two angles and the included

side of one triangle equal to the

corresponding angles and

included side of another triangle

then the two triangles are

congruent. By ASA postulate.