1. Yes, ΔABC and ΔDEF are similar triangles by SSS similarity.
2. Yes, ΔABC and ΔFGH are similar triangles by AAA similarity.
Solution:
Question 1.
(a) Yes, ΔABC and ΔDEF are similar triangles.
(b) <em>If two triangles are congruent, then their corresponding sides are in the same ratio.</em>
Let's compare the sides of the triangles.
Corresponding sides of the triangle are in the same ratio.
Hence by SSS similarity ΔABC and ΔDEF are similar triangles.
Question 2:
(a) Yes, ΔABC and ΔFGH are similar triangles.
By triangle sum theorem,
In triangle ABC,
m∠A + m∠B + m∠C = 180°
m∠A + 81° + 52° = 180°
m∠A = 180° – 133°
m∠A = 47°
In triangle ABC,
m∠F + m∠G + m∠H = 180°
47° + m∠G + 52° = 180°
m∠G = 180° – 99°
m∠G = 81°
Yes, ΔABC and ΔFGH are similar triangles.
(b) <em>If two triangles are congruent, then their corresponding angles are congruent.</em>
∠A ≅ ∠F
∠B ≅ ∠G
∠C ≅ ∠H
Hence by AAA similarity ΔABC and ΔFGH are similar triangles.