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Proving Vertical Angles Are Congruent
Given: 22 and 24 are vertical angles.
Prove: 22 24
4
1
3
m
2
12
Assemble the proof by dragging tiles to
the Statements and Reasons columns.
Statements Reasons
mL2+ m23 = 180
22 and 23 are a linear pair
Statements
m23+ m24 = 180
23 and 24 are a linear pair
Reasons
22 and 24 are vert. angles
mL2+ m23= m/3 +
m24

Answer 1

In this proof, the task is to demonstrate that Vertical Angles are congruent. See the explanation below.

What is a vertical angle?

When two lines intersect at a location, vertical angles are generated. They are always on equal footing. In other words, four angles are generated anytime two lines cross or meet. We can see that two opposed angles are equal, and they are referred to as vertical angles.

Hence the proof is given as follows:

1. < 2 & < 4 are vert. angles                    Given

2. Lines M & N intersect at P                  Definition of vertical angles

3. < 2 & < 3 are a linear pair                   Def of linear angles

4. m < 2 + m < 3 = 180                             Angle Addition postulate

5. <3 and < 4 are a linear pair                Definition of a linear pair

6. m < 3 + m <4 =180                               Angle of addition postulate

7. m < 2 + m < 3 = m < 3 + m < 4             Substitution property

8. m < 2 = m < 4                                       Subtraction property    

9. < 2 ≅ <4                                               Definition of congruent angles

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