Question

Exterior angle bisector theorem right angle triangle

Answer 1

Answer:

Step-by-step explanation:

Dear Mark me brain list ❤️❤️❤️

Exterior angle bisector theorem : The external bisector of an angle of a triangle divides the opposite side externally in the ratio of the sides containing the angle.

Given : A ΔABC, in which AD is the bisector of the exterior ∠A and intersects BC produced in D.

Prove that : BD / CD = AB / AC

Construction : Draw CE || DA meeting AB in E.

Statements Reasons

1) CE || DA 1) By construction

2) ∠1 = ∠3 2) Alternate interior

angle

3) ∠2 = ∠4 3) Corresponding angle

(CE ||DA and BK is a

transversal

4) AD is a

bisectorof ∠A. 4) Given

5) ∠1 = ∠2 5) Definition of angle

bisector

6) ∠3 = ∠4 6) Transitivity (from 2

and 4)

7) AE = AC 7) If angles are equal

then side opposite to

them are also equal

Answer 2

Answer:

Step-by-step explanation:

Dear Mark me brain list ❤️❤️❤️

Exterior angle bisector theorem : The external bisector of an angle of a triangle divides the opposite side externally in the ratio of the sides containing the angle.

Given : A ΔABC, in which AD is the bisector of the exterior ∠A and intersects BC produced in D.

Prove that : BD / CD = AB / AC

Construction : Draw CE || DA meeting AB in E.

Statements Reasons

1) CE || DA 1) By construction

2) ∠1 = ∠3 2) Alternate interior

angle

3) ∠2 = ∠4 3) Corresponding angle

(CE ||DA and BK is a

transversal

4) AD is a

bisectorof ∠A. 4) Given

5) ∠1 = ∠2 5) Definition of angle

bisector

6) ∠3 = ∠4 6) Transitivity (from 2

and 4)

7) AE = AC 7) If angles are equal

then side opposite to

them are also equal