Question

Please help!!

AD¯¯¯¯¯ is an altitude, and ∠BAC ​ is a right angle. --> given
∠ADB ​ and ∠ADC are right angles. --> Definition of altitude
∠BAC≅∠BDA ​ ----> ???
∠BAC≅∠ADC

∠B≅∠B ---> AA Similarity Postulate
∠C≅∠C
ABBD=CBAB ---> ???
(AB)2=(CB)(BD) ​ Cross multiply and simplify.
ACDC=CBAC Polygon Similarity Postulate
​ (AC)2=(CB)(DC) ​ Cross multiply and simplify.
​ (AB)2+(AC)2=(AB)2+(CB)(DC) ​ Addition Property of Equality
​ (AB)2+(AC)2=(CB)(BD)+(CB)(DC) ​ Substitution Property of Equality
​ (AB)2+(AC)2=(CB)(BD+DC) ​ ---> ???
BD+DC=CB Segment Addition Postulate
​ (AB)2+(AC)2=(CB)2 ​ Substitution Property of Equality

Answer 1

1) All right angles are congruent

2) Polygon similarity postulate

3) distributive property of equality

I took the test

Answer 2

see below

Explanation:

The figure below shows the selections I would make.

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You can choose "polygon similarity postulate" for the second blank based on that step's similarity to the one two steps down from it.

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Strictly speaking, the distributive property is a property of multiplication over addition. It is not a property of equality.