Question

given: isosceles trapezoid abcd with diagonals $overline{bd}$ and $overline{ac}$. prove: $overline{ac}congoverline{bd}$. statement reason isosceles trapezoid abcd with diagonals $overline{bd}$ and $overline{ac}$. given $overline{ad}congoverline{bc}$ definition of isosceles trapezoid $overline{dc}congoverline{dc}$ reflexive property of congruence $angle adccongangle bcd$ base angles of an isosceles trapezoid are congruent $\triangle adccong\triangle bcd$? $overline{ac}congoverline{bd}$ cpctc identify the missing reason in the proof. a. aas theorem b. sas criterion c. sss criterion d. asa criterion

Explanation:

Step1: Recall congruent - triangle criteria

We have $\overline{AD}\cong\overline{BC}$ (from the definition of isosceles trapezoid), $\angle ADC\cong\angle BCD$ (base - angles of isosceles trapezoid) and $\overline{DC}\cong\overline{DC}$ (reflexive property).

Step2: Identify the congruence criterion

Two sides and the included angle of $\triangle ADC$ are congruent to two sides and the included angle of $\triangle BCD$. This satisfies the Side - Angle - Side (SAS) congruence criterion.

Answer:

B. SAS criterion