Question

Move words to the blanks and equations to the boxes to prove that vertical angles <21 and <23 are congruent.

Answer 1

See proof below

Explanation:

From the given diagram, we can see that <2 and <3 lies on the same straight line, hence the sum of the angles is 180 degrees (supplementary)

<2 + <3 = 180 .... 1

Similarly. <1 and <2 are also supplementary angles

<1 + <2 = 180 .... 2

Subtract 1 from 2;

<3 - < 1 + <2 - <2 = 180 - 180

<3 - <1 +0 = 0

<3 - <1 = 0

Add <1 to both sides

<3 - <1 + <1 = 0+<1

<3 = <1 (Proved!)

This shows that <3 and <1 are equal

We can also conclude that <3 and <1 are vertically opposite angles and vertically opposite angles are equal