Question

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 1. AB ⊥ BD, AB ⊥ BC, AC = AD Perpendicular Lines Form Right Angles 2. ∠ABC and ∠ABD are right angles Reflexive Property of Equality 3. AB = AB Hypotenuse - Leg Postulate 4. △ABC ≅ △ABD Given

Answer 1

Answer:

1) AB ⊥ BD, AB ⊥ BC, AC = AD Reason: Perpendicular Lines Form Right Angles

2) ∠ABC and ∠ABD are right angles

3) AB = AB Reason: Reflexive Property of Equality.

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

Step-by-step explanation:

Given: AB ⊥ BD AB ⊥ BC AC = AD Prove: △ABC ≅ △ABD 1. AB ⊥ BD, AB ⊥ BC, AC = AD

1) AB ⊥ BD, AB ⊥ BC, AC = AD Reason: Perpendicular Lines Form Right Angles

If there are perpendicular lines between the line segment AB and BD, check the graph below, then this pair of line segment form a perpendicular line.

2) ∠ABC and ∠ABD are right angles

Notice that the hypotenuses are congruent. We should say AC ≅ AD. This information is vital for the Hypotenuse Leg Theorem.

3) AB = AB Reason: Reflexive Property of Equality.

Reflexive Property of Equality says that each line segment, angle or shape is congruent to itself.

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

If two right triangles with congruent hypotenuses and one congruent leg then, we can say these two triangles are congruent ones. The proof of this Theorem is obtained by the Pythagorean Theorem, and then by side side side congruence, we can be sure both triangles are congruent.