Answer:
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