Fill in the blanks to complete this proof of theorem 2-3.

If two congruent angles are complements of the same angle, then the two angles are congruent.

Given: angle 1 and angle 2 are complementary

angle 3 and angle 2 are complementary

Prove: angle 1 is congruent to angle 3

Proof: angle 1 and angle 2 are complementary and angle 3 and angle 2 are complementary because it is given. By the definition of complementary angles, m of angle 1 + m of angle 2 = ___ and m of angle 3 + m of angle 2 = ___. Then m of angle 1 + m of angle 2 = m of angle 3 + m of angle 2 by the Transitive Property of Equality. Subtract m of angle 2 from each side. By the Subtraction Property of Equality, you get m of angle 1 = ___. Angles with the same measure are ___, so angle 1 is congruent to angle 3.

Therefore.

angle 1 is congruent to angle 3 ...Proved

The proof with steps are below with Fill in the blanks

Step-by-step explanation:

Complementary Angles:

Two angles are Complementary when they add up to 90 degrees.

Example 40° and 50° are Complementary Angles.

If 'x' and 'y' are Complementary Angles the we have

Here,

Given:

angle 1 and angle 2 are complementary

angle 3 and angle 2 are complementary

To Prove:

angle 1 is congruent to angle 3

Proof:

Step 1:

angle 1 and angle 2 are complementary and angle 3 and angle 2 are complementary because it is Given.

Step 2:

By the definition of complementary angles,

m of angle 1 + m of angle 2 = _90°__ and m of angle 3 + m of angle 2 = _90°_.

Step 3:

Transitive Property of Equality.

Then m of angle 1 + m of angle 2 = m of angle 3 + m of angle 2 by the Transitive Property of Equality.

Step 4:

Subtract m of angle 2 from each side. By the Subtraction Property of Equality, you get

m of angle 1 = _measure of angle_3_.

Step 5:

Angles with the same measure are _Congruent__,

Step 6:

so angle 1 is congruent to angle 3.

Therefore.

angle 1 is congruent to angle 3 ...Proved

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