181k views
1 vote
Prove the Following! Need help ASAP!

Prove the Following! Need help ASAP!-example-1
User Podkova
by
7.8k points

2 Answers

6 votes

Answer:

Since AD is the angle bisector of ∠A and ΔABC is an isosceles triangle:

=> AD ⊥ BC

=> ∠ADB = ∠ADC = 90°

We have: ∠BAD = ∠CAD (AD is an angle bisector of ∠A)

∠ADB = ∠ADC = 90°

Both triangles have AD in common

=> ΔABD ≅ ΔACD

User Okan Aslankan
by
8.4k points
3 votes

Answer:

Given:

ΔABC is an isosceles triangle

AD is an angle bisector of ∠A

Statement | Proof

____________________________________________________

ΔABC is an isosceles triangle Given; Definition of an

isosceles triangle.

AD bisects ∠ABC Definition of a angle bisector.

AD ≅ AD Reflexive Property

AD bisects BC Definition of a line segment bisector

BD ≅ CD " "

∠BDA ≅ ∠ADC Triangle Bisector Theorem

What has been proven so far:

AD ≅ AD ; ∠BDA ≅ ∠CDA ; BD ≅ CD

Based on this information,

ΔABD ≅ ΔACD Side-Angle-Side Theorem

_____________________________________________________

~

User Skurpi
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories