Congruent Figures at a Glance

Triangles ABC and DEF are congruent. Name a pair of corresponding sides and a pair of corresponding angles.

The pairs of corresponding sides are:
AB and DE
BC and EF
CA and FD

The pairs of corresponding angles are:
∠A and ∠D
∠B and ∠E
∠C and ∠F

Triangles ABC and DEF are congruent. If AB is 3 ft long and m∠A = 20° how long is DE and what is m∠D?

The corresponding sides of congruent figures have the same length. In other words, the matching sides are the same length. Since AB corresponds to DE, and AB is 3 ft long, then DE is also 3 ft long.

The corresponding (or matching) angles are also the same measure. If m∠A = 20°, then m∠D = 20°.

Triangles ABC and DEF are congruent isosceles triangles. If m∠A = 50°, what is m∠E?

Angles A and D are corresponding angles so they are congruent. If m∠A = 50°, then m∠D = 50°.

Triangles ABC and DEF are congruent isosceles triangles. If m∠A = 50°, find the measurement of Angle E.

Angles A and D are corresponding angles so they are congruent. If m∠A = 50°, then m∠D = 50°.

Since triangle DEF is an isosceles triangle, we know that m∠E and m∠F are equal.

We also know that the sum of m∠D + m∠E + m∠F = 180°.

Since m∠D = 50°, then m∠E + m∠F = 180° – 50° which is 130°.

We know that m∠E equals m∠F and both angles add to 130° so m∠E = .

And just like that, m∠ E = 65°.