maritzafreeman7
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Given: Z1 is complementary to 22.
What is the missing statement in step 3 of the proof?
22 is complementary to 23.
0 m21 = m22
Prove: mz1 = m 23
OmZ1 + m22 = 90°
OmZ2 = m23
VV
m22 + m23 = 180°
Statements
1. 21 is comp. to 22
2. 22 is comp. to 23
3. ?
4. m21-90°-m22
5 m22+m23-90°
6. m23-90°-m22
7. m 1 m3
1
2.
3
4
5
6.
7
Reasons
given
given
def. of comp. ZS
subtr. equality prop.
def. of comp. ZS
subtr. equality prop
trans. prop.

Given Z1 is complementary to 22 What is the missing statement in step 3 of the proof 22 is complementary to 23 0 m21 m22 Prove mz1 m 23 OmZ1 m22 90 OmZ2 m23 VV class=

Respuesta :

Answer:

Option (2)

Step-by-step explanation:

                          Statements                                Reasons

1). ∠1 is comp. to ∠2                                1. Given

2). ∠2 is comp. to ∠3                              2. Given

3). ∠1 + ∠2 = 90°                                      3. def. of comp. angles

4). m∠1 = 90° - ∠1                                    4. Subtr. equality property

5). m∠2 + m∠3 = 90°                              5. def. of comp. angles

6). m∠3 = 90° - m∠2                               6. subtr. equality property

7). m∠1 = m∠3                                         7. Transitive property

Option (2) will be the answer.

Both angle ∠1 and ∠3 are complementary to ∠2, therefore, ∠1 + ∠2 = 90°

and by properties of equality, ∠1 = ∠3.

Response:

  • The missing statement in step 3 is; m∠1 + m∠2 = 90°

Which property or definition is used to find the missing statement?

The completed two column proof is presented as follows;

Statements  [tex]{}[/tex]                             Reasons

1. ∠1 is comp. to ∠2  [tex]{}[/tex]               1. Given

2. ∠2 is comp. to ∠3  [tex]{}[/tex]             2. Given

  • 3. m∠1 + m∠2 = 90°  [tex]{}[/tex]               3. Definition of complementary angles

4. m∠1 = 90° - m∠2  [tex]{}[/tex]                4. Subtraction equality property

5. m∠2 + m∠3 = 90°  [tex]{}[/tex]              5. Definition of complementary angles

6. m∠3 = 90° - m∠2  [tex]{}[/tex]                6. Subtraction equality property

7. m∠1 = m∠2   [tex]{}[/tex]                        7. Transitive property

  • The missing statement in step 3 is therefore; m∠1 + m∠2 = 90°

Details of the solution:

Given that ∠1 is complementary to ∠2, we have;

∠1 + ∠2 = 90°

Similarly, by definition of complementary angles, we have;

∠2 + ∠3 = 90°

Which gives;

∠3 + ∠2 = 90°

Therefore;

∠1 + ∠2 = ∠3 + ∠2

Subtracting ∠2 from both sides (subtraction property of equality), gives;

∠1 + ∠2 - ∠2 = ∠3 + ∠2 - ∠2

∠1 + 0 = ∠3 + 0

Which gives;

∠1 = ∠3

Learn more about properties of equality here

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