∠ABC and ∠ABD are a linear pair. Prove that m∠ABC + m∠ABD = 180°.
paragraph proof
huh? That's the definition of a linear pair.
To prove that the sum of the angles ∠ABC and ∠ABD is equal to 180°, we need to use the given information that ∠ABC and ∠ABD form a linear pair.
A linear pair consists of two adjacent angles whose measures add up to 180 degrees. In this case, the angles ∠ABC and ∠ABD share a common ray (AB) and form a straight line, or a straight angle.
To begin the paragraph proof, we can state the given information:
Given: ∠ABC and ∠ABD are a linear pair.
To prove: m∠ABC + m∠ABD = 180°.
Proof:
Since ∠ABC and ∠ABD form a linear pair, they share a common ray (AB) and form a straight angle.
Therefore, we can conclude that m∠ABC + m∠ABD = 180°, based on the definition of a linear pair and the fact that the angles ∠ABC and ∠ABD form a straight angle.
This completes the paragraph proof.