Question

Complete the proof of the exterior angle theorem.

Given: angle ACD is an exterior angle of triangle BCD.


Prove: angle B + angle C = angle ADC


Statements:

1. angle ADC is an exterior angle of triangle BCD

2.

3. angle ADC and angle BCD form a linear pair

4.

5.

6.

7. angle ADC = angle B + angle C


Reasons:

1. Given

2. Triangle Sum Theorem

3.

4.

5.

6.

7. Subtraction Property of Equality


(i need the blanks filled in)

Answer 1

Explanation:

From the attached diagram below,

< ADC + <D = 180° (sum of linear angle) ------------(1)

<B + <C + <D = 180° (sum of interior angle in a triangle)---------(2)

Since the two equations are equal to 180°, We equate the two equation

i.e

(1) = (2)

< ADC + <D = <B + <C + <D

<D from the left hand side will cancel <D on the right hand side

We are now left with

<ADC = <B + <C