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) If two triangles are congruent, then their corresponding sides are in the same ratio.
Let's compare the sides of the triangles.
[tex]$\frac{AB}{DE} =\frac{8}{6}=\frac{4}{3}[/tex]
[tex]$\frac{BC}{EF} =\frac{12}{9}=\frac{4}{3}[/tex]
[tex]$\frac{AC}{DF} =\frac{16}{12}=\frac{4}{3}[/tex]
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) If two triangles are congruent, then their corresponding angles are congruent.
∠A ≅ ∠F
∠B ≅ ∠G
∠C ≅ ∠H
Hence by AAA similarity ΔABC and ΔFGH are similar triangles.
