Complete the two-column proof.
DiagramTwo horizontal lines that appear to be parallel are cut by a transversal. Where the transversal intersects the top horizontal line, the angle in the top right corner is obtuse and labeled with a 2. Where the transversal intersects the bottom horizontal line, the angle in the top left corner is acute and labeled with a 1, the angle in the bottom left corner is obtuse and labeled with a 4, and the angle in the bottom right corner is acute and labeled with a 3.
Drawing not to scale.
Given: Angle 2 is congruent to angle 4, the measure of angle 2 is 110 degrees
Prove: m angle D equals 70 degrees
Statement Proof
Angle 2 is congruent to angle 4, the measure of angle 2 is 110 degrees Given
measure of angle 2 equal to measure of angle 4 Definition of congruent angles
m angle 4 equals 110 degrees a.
m angle 3 and m angle 4are a linear pair Definition of a linear pair (shown in diagram)
m angle 3 and m angle 4are supplementary Linear Pair Postulate
m angle 3 plus m angle 4 equals 180 degrees b.
m angle 3 plus 110 degrees equals 180 degrees Substitution Property
m angle D equals 70 degrees c.
(3 points)
a. m angle 4 equals 110 degrees Given
b. m angle 3 and m angle 4 are a linear pair Definition of a linear pair (shown in diagram)
c. m angle 3 and m angle 4 are supplementary Linear Pair Postulate
d. m angle 3 plus m angle 4 equals 180 degrees Definition of supplementary angles
e. m angle 3 plus 110 degrees equals 180 degrees Substitution, using the given information that m angle 2 equals 110 degrees
f. m angle 3 equals 70 degrees Subtraction Property of Equality, subtracting 110 degrees from both sides
g. m angle D equals 70 degrees Substitution, since angle D and angle 3 are opposite angles and therefore have equal measures.