Question

10 POINT TO WHOEVER HELPS ME!! URGENT

1. Write a paragraph proof for the following conjecture.
2
Given: < 1 and <3 are vertical angles

prove: <1 congruent to <3

Answer 1

<1 ≅ <3 (congruence property)

Explanation:

Given that: <1 and <3 are vertical angles.

Prove: <1 congruent to <3

Vertical angles are angles that are vertically opposite, and are formed under the same conditions. Thus, they are always congruent.

<1 + <2 =
`180^(o)` (sum of angles on a straight line)

Also,

<2 + <3 =
`180^(o)` (sum of angles on a straight line)

So that,

<1 + <2 ≅ <2 + <3 =
`180^(o)`

Thus, we can say that;

<1 + <2 ≅ <2 + <3

Since <2 is a common angle on both sides, then;

<1 ≅ <3 (congruence property)