Question

In the diagram below, angle ABC = DEF. If AB=6 and AC=8, which statements will justify similarity by SAS? Explain

(A) DE=12, DF=16 and angle A ~= angle D
(B) DE=8,DF=10 and angle A ~= angle D
(C) DE=36, DF=64 and angle C ~= angle F
(D) DE=15, DF=20 and angle C~= angle F

Answer 1

The correct choice is (B) DE = 8, DF = 10, and ∠A ≅ ∠D.

Side-Angle-Side (SAS) similarity criterion states that if two triangles have two pairs of corresponding sides that are proportional and the included angles are congruent, then the triangles are similar.

In this case, the sides AB and AC of the smaller triangle ABC are proportional to the sides DE and DF of the larger triangle DEF. This corresponds to the given information in choice (B) where DE = 8 and DF = 10. Additionally, the angles ∠A and ∠D are congruent, ensuring the SAS criterion is satisfied.

Therefore, based on the SAS similarity criterion, the correct choice is (B) DE = 8, DF = 10, and ∠A ≅ ∠D, justifying the similarity between triangles ∆ABC and ∆DEF.