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Match 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

help?

Respuesta :

asadullahgiki
Concept:
When we show the congruency between two right triangles having equal hypothesis then we use the Hypothesis-Leg ( HL) theorem.

Solution:

Given that 
                  m AC = m AD ( measure of hypothesis of one right triangle is                                                     equal to the measure of hypothesis of other                                                       triangle)
As, AB ⊥ BD and also AB ⊥ BC
So, 
                  AB ≅ AB   ( side(leg) is self congruent ) 
Now,
According to HL(Hypothesis-Leg ) theorem △ABC ≅ △ABD.

Answer:

1. AB ⊥ BD, AB ⊥ BC, AC = AD; given

2. ∠ABC and ∠ABD are right angles; perpendicular lines form right angles

3. AB = AB; reflexive property of equality

4. △ ABC ≅ △ ABD; hypotenuse- leg postulate

Step-by-step explanation:

simple geometry....

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