1. Complete the paragraph proof
Given: ∠A and ∠B are complementary, and ∠B and ∠C are complementary
Prove: ∠A ≌ ∠C
By definition of complementary angles, m∠A + _____ = 90° and m∠B + m∠C+ _______.
Then, m∠A + m∠B = m∠B + m∠C by the _____________________________. Subtract
m∠B from each side. You get ________= m∠C or _________ ≅ ∠C
steve we literally don’t care about geometry we’re just doing our best to pass the class (might i add in a global pandemic) we have other things to attend to. so if you aren’t going to answer respectfully just shut up man.
To complete the paragraph proof, we will use the definitions and properties of complementary angles.
By definition of complementary angles, we know that the measures of ∠A and ∠B add up to 90°. So, we can write the first statement as:
By definition of complementary angles, m∠A + _____ = 90°.
Similarly, we also know that the measures of ∠B and ∠C add up to 90°. So, we can write the second statement as:
By definition of complementary angles, m∠B + m∠C+ _______.
Since we want to prove that ∠A ≌ ∠C, we can start by observing that we have m∠A + m∠B = m∠B + m∠C. This statement is based on the fact that both ∠A and ∠B have the same complement, which is ∠C.
Now, to simplify the equation, we can subtract m∠B from each side:
m∠A + m∠B - m∠B = m∠B + m∠C - m∠B.
This simplifies to:
m∠A = m∠C.
Therefore, we can conclude that ∠A ≌ ∠C, and we can write it as:
∠A ≌ ∠C or ∠A ≅ ∠C.