Question

deltamath back to home triangle proofs complete: 54% no late credit grade: 0% interior and exterior triangle angles triangle congruence criteria triangle congruence, basic flowchart proof triangle congruence, flowchart proof triangle 1 (level 1) bd bisects ac reason: given ad ≅ cd reason: select reason ∠a ≅ ∠c reason: select reason ab ≅ cb reason: select reason △abd ≅ △cbd reason: select reason answer attempt 1 out of 2 submit answer

Explanation:

Step1: Definition of bisect

If a line bisects a line - segment, it divides the line - segment into two equal parts. Since $\overline{BD}$ bisects $\overline{AC}$, by the definition of a bisector, $\overline{AD}\cong\overline{CD}$.

Step2: Given information

We are given that $\angle A\cong\angle C$ and $\overline{AB}\cong\overline{CB}$.

Step3: SAS (Side - Angle - Side) congruence criterion

In $\triangle ABD$ and $\triangle CBD$, we have $\overline{AD}\cong\overline{CD}$ (from Step 1), $\angle A\cong\angle C$ (given), and $\overline{AB}\cong\overline{CB}$ (given). So, by the SAS congruence criterion, $\triangle ABD\cong\triangle CBD$.

Answer:

• $\overline{AD}\cong\overline{CD}$ Reason: Definition of bisector
• $\angle A\cong\angle C$ Reason: Given
• $\overline{AB}\cong\overline{CB}$ Reason: Given
• $\triangle ABD\cong\triangle CBD$ Reason: SAS (Side - Angle - Side) congruence criterion