∠ABC and ∠ABD are a linear pair. Prove that m∠ABC + m∠ABD = 180°.
Write a paragraph proof
To prove that the sum of angles ∠ABC and ∠ABD is 180°, we will use the fact that they form a linear pair. A linear pair consists of two adjacent angles that together form a straight line, which means they have a common vertex and their non-common sides form a straight line. In this case, the common side is AB.
Let's start the proof by drawing a line segment AB. Next, we extend a line from segment AB to form a straight line CD, with D as an arbitrary point. Now, we have two adjacent angles, ∠ABC and ∠ABD, that are formed by the intersection of line AB and line CD.
Since ∠ABC and ∠ABD are a linear pair, the sum of their measures should be equal to the measure of a straight angle, which is 180°. This can be justified using the angle addition postulate, which states that if two angles are adjacent, their measures can be added to find the measure of the larger angle they form.
Therefore, we can conclude that m∠ABC + m∠ABD = 180°, as required.