Question

sylvia plans to use the marked triangle to help prove that the base angles of an isosceles triangle are congruent. what basic strategy should she use in her proof? (1 point) sylvia should prove that △acd≅△abd by the sss congruence theorem and therefore ∠c≅∠b by the cpctc theorem. sylvia should prove that △acd≅△abd by the sas congruence theorem and therefore ∠c≅∠b by the cpctc theorem. sylvia should prove that ∠c≅∠b by the base angles theorem. sylvia should prove that (overline{ad}congoverline{ad}) by the reflexive property of congruence and therefore ∠c≅∠b by the cpctc theorem.

Explanation:

In the figure, we can see two - triangles $\triangle ACD$ and $\triangle ABD$. There are two pairs of congruent sides (the marked segments) and a common side $AD$. The Side - Angle - Side (SAS) Congruence Theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. Here, $\angle CDA\cong\angle BDA$ (the marked angles), $AC = AB$ (marked segments) and $AD=AD$ (common side). Once we prove $\triangle ACD\cong\triangle ABD$ by SAS, we can use the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) Theorem to show that $\angle C\cong\angle B$.

Answer:

Sylvia should prove that $\triangle ACD\cong\triangle ABD$ by the SAS Congruence Theorem and therefore $\angle C\cong\angle B$ by the CPCTC Theorem.