Let's begin by looking at the given information and what we want to prove.
Given:& ∠ ABC is a right angle
Prove:& ∠ ABD and ∠ CBD are complementary
To prove that ∠ ABD and ∠ CBD are complementary, we will first analyze the given graph. The information, that ∠ ABC is a right angle, tells us that m∠ ABC=90. Now, let's highlight the right angle in the diagram.
Notice that D is in the interior of ∠ A B C. Hence, we can use the Angle Addition Postulate to rewrite m∠ ABC as the sum of two smaller angles. We will recall the postulate.
Angle Addition Postulate
If two angles have the same vertex and are side by side, the new angle formed measures the sum of the two side by side angles.
In our case ∠ ABD and ∠ CBD have the same vertex B and are side by side, so m∠ ABC need to be the sum of m∠ ABD and m∠ CBD.
m∠ ABD + m∠ CBD = m∠ ABC
With this information, we can proceed and write a two-column proof.
