Question

Write a paragraph proof for the Vertical Angles Theorem (hint: draw a pair of vertical angles and label each angle using numbers or letters)
Does anyone know what the heck this means? Im lost

Answer 1

First State the vertical angles theorem.

Answer 2

Vertical angles are always congruent.
So you want to prove that vertical angles are always congruent. So you begin with a pair of vertical angles.

Answer 3

So, first I write down the theorem? and then draw vertical angles?

Answer 4

No I'm saying you need to first know what you are trying to prove. So you begin with the illustration

Answer 5

Proof: (start)
Let angle 1 and angle 2 be vertical angles.

Answer 6

Can you think of what you can use to show that angle 1 and angle 2 equal each other??? Hint: Supplementary angles

Answer 7

That is what you want to show

Answer 8

By the supplementary property
measure of angle 1 + measure of angle 3= 180 degrees
Similarly,
measure of angle 2+ measure of angle 3 =180 degrees

Answer 9

thanks a lot!

Answer 10

now subtract measure of angle 3 from both sides of each equation:
measure of angle 1=180-measure of angle 3
measure of angle 2=180-measure of angle 3

Answer 11

using a similar argument you show that measure of angle 3=measure of angle 4

Answer 12

does it make sense?

Answer 13

sort of...

Answer 14

we showed
measure of angle 1=180-measure of angle 3
measure of angle 2=180-measure of angle 3
so measure of angle 1=measure of angle 2

Answer 15

alright