Given: 22 and 24 are vertical angles. Prove: 2224
Statements Reasons
m22+ m23 = 180
m23 + m 24 = 180
22 and 24 are vert angles
22 and 23 are a linear
lines m and n intersect at P
m
pair
23 and 24 are a linear
pair
Reasons
1
Statements
N
n
4
3
Assemble the proof by dragging tiles to
the Statements and Reasons columns.

Step-by-step explanation:

Given:

∠2 and ∠4 are the vertical angles

To prove:

∠2 ≅ ∠4

Solution:

                Statements                                          Reasons

1). ∠2 and ∠4 are the vertical angles      1). Given

2). Lines m and n intersect at P.             2). Definition of vertical angles

2). ∠2 and ∠3 are the linear pairs          2). Given in the diagram

3). ∠2 + ∠3 = 180°                                    3). Linear pair theorem

4). ∠3 and ∠4 are the linear pairs          2). Given in the diagram

5). ∠3 + ∠4 = 180°                                    5). Linear pair theorem

6). ∠2 + ∠3 = ∠3 + ∠4                             6). Transitive Property

7). ∠2 ≅ ∠4                                              7). Subtraction property

1/4 and 8/3 because:

the reciprocal if 4 is 1/4 because 4 is used as 4/1 and the opposite of that is 1/4. the opposite of 3/8 is 8/3 so that is the answer.