Complete the proof. help me answer this please!!

Question

asked Oct 20, 2021 170k views

1 Answer

Rovdjuret · Answer 1 · 2021-10-24T02:33:09+0000

Answer:

2. Definition of supplementary angles

3.
$\angle 1 + \angle 2 = \angle 1 + \angle 3$

4.
$\angle 2 = \angle 3$

5. Definition of congruent angles

Explanation:

Required

Fill in the gaps

1. Given

Supplementary angles:
$\angle 1$ and
$\angle 2$

Supplementary angles:
$\angle 1$ and
$\angle 3$

2. Supplementary angles add up to 180.

So:

$\angle 1 + \angle 2 = 180$

$\angle 1 + \angle 3 = 180$

3. Apply transitive property on (2)

$\angle 1 + \angle 2 = 180$ and
$\angle 1 + \angle 3 = 180$ , then

$\angle 1 + \angle 2 = \angle 1 + \angle 3$

4. Subtract
$\angle 1$ from both sides

$\angle 1 - \angle 1 + \angle 2 = \angle 1 + \angle 3 - \angle 1$

$\angle 1 - \angle 1 + \angle 2 = \angle 1 - \angle 1+ \angle 3$

$\angle 2 = \angle 3$

This property is called the subtraction property

5. If
$\angle 2 = \angle 3$ ,

Then
$\angle 2$ and
$\angle 3$ are congruent