Question

Leg-Leg TheoremMatch the reasons with the statements in the proof to prove that triangle ABC is congruent to triangle ABD, given that AB ⊥ BD, AB ⊥ BC, and AC = AD. Given: AB ⊥ BD AB ⊥ BC AC = AD Prove: △ABC ≅ △ABD

1. ∠3 and ∠4 are right angles, AX = BX


2. CX = CX
3. △AXC ≅ △BXC

Given
Reflexive Property of Equality
Leg-Leg Theorem

Answer 1

1.) AB ⊥ BD, AB ⊥ BC, AC = AD --- d.) Given

2.) ∠ABC and ∠ABD are right angles --- c.) Perpendicular Lines Form Right Angles

3.) AB = AB --- a.) Reflexive Property of Equality

4.) △ABC ≅ △ABD --- b.) Hypotenuse - Leg Postulate

Explanation:

1.) AB ⊥ BD, AB ⊥ BC, AC = AD

2.) ∠ABC and ∠ABD are right angles

3.) AB = AB

4.) △ABC ≅ △ABD

a.) Reflexive Property of Equality

b.) Hypotenuse - Leg Postulate

c.) Perpendicular Lines Form Right Angles

d.) Given

Answer 2

Answer: The answers to the steps are the same order that is given at the bottom of your question.

1) Given, these statements are given in the problem.
2) Reflective property, sides are always congruent to themselves. (You have the letters different than the problems, I think just a typo)
3) Leg-Leg Theorem, If two legs of a right triangle are congruent, then the triangles are congruent.