Question

For the triangles described, which of the following statements must be true? In triangle DEF, DE=8 in., DF=23 in., and ∡D=16°. In triangle PQR, PQ=23 in., PR=8 in., and ∡P=16°. (1 point) ∠Q≅∠F ∠R≅∠F DE¯¯¯¯¯¯¯¯≅PQ¯¯¯¯¯¯¯¯ ∠E≅∠Q

Answer 1

∠Q≅∠F

Explanation:

Two triangles are said to be congruent if all the three sides of the triangles are equal and all the three angles are equal.

Given that: In triangle DEF, DE=8 in., DF=23 in., and ∡D=16°. In triangle PQR, PQ=23 in., PR=8 in., and ∡P=16°.

Hence we can say that ΔDEF is congruent to ΔPQR. According to the side-angle-side (SAS) triangle congruence theorem: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

Therefore:

DF = PQ, DE = PR, EF = RQ, ∠D = ∠P, ∠E = ∠R and ∠F = ∠Q