Question

determine the
easons\ for each statement made (you may use the same reason multiple times) in order to complete the following proof.
step 1: ∠a≅∠c, bd bisects ∠abc
step 2: ∠abd≅∠cbd
step 3: bd≅bd
step 4: △abd≅△cbd
answer
attempt 1 out of 3
step 1 reason =
step 2 reason =
step 3 reason =
step 4 reason =

Explanation:

Step1: Given

Given in the problem - statement.

Step2: Definition of angle - bisector

If a ray bisects an angle, it divides the angle into two congruent angles.

Step3: Reflexive property of congruence

Any segment is congruent to itself.

Step4: Angle - Angle - Side (AAS) congruence criterion

We have ∠A≅∠C, ∠ABD≅∠CBD, and BD≅BD, so by AAS, △ABD≅△CBD.

Answer:

Step 1 Reason = Given
Step 2 Reason = Definition of angle - bisector
Step 3 Reason = Reflexive property of congruence
Step 4 Reason = Angle - Angle - Side (AAS) congruence criterion