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Copy everything shown and write a two-column proof.

Given: m1=m2; m3=m4.

Prove:YSXZ

Short Answer

Expert verified

The two-column proof is:

Statements

Reasons

m1=m2

Given

m3=m4

Given

m1+m2+m3+m4=180°

The angles ∠3,∠1, ∠2 and ∠4 form the straight angle

m1+m1+m3+m3=180°

Substitution property

2m1+m3=180°

Combine the like terms

m1+m3=90°

Divide both sides by 2.

mSYX=90°

Complementary angles

YSXZ

Definition of perpendicular lines

Step by step solution

01

Step 1. Observe the diagram.

The given diagram is:

02

Step 2. Description of step.

It is being given that m1=m2and m3=m4.

From the given diagram it can be noticed that angles ∠3, ∠1, ∠2 and ∠4 form the straight angle.

Therefore, m1+m2+m3+m4=180°.

Now, by using the substitution property it can be obtained that:

m1+m1+m3+m3=180°2m1+m3=180°m1+m3=180°2m1+m3=90°

Therefore, mSYX=90°.

Therefore, by using the definition of perpendicular lines it can be said that YSXZ.

Hence proved.

03

Step 3. Description of step.

Statements

Reasons

m1=m2

Given

m3=m4

Given

m1+m2+m3+m4=180°

The angles∠3,∠1,∠2 and∠4forms the straight angle

m1+m1+m3+m3=180°

Substitution property

2m1+m3=180°

Combine the like terms

m1+m3=90°

Divide both sides by 2.

mSYX=90°

Complementary angles

YSXZ

Definition of perpendicular lines

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