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)
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 4 are a linear pair Definition of a linear pair (shown in diagram)
m angle 3 and m angle 4 are 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.
Angle 2 and angle 3 are corresponding angles, the measure of angle 2 is 110 degrees Given
m angle 2 equals m angle 3 Definition of corresponding angles
m angle 3 equals 110 degrees Substitution Property
m angle 3 plus m angle 4 equals 180 degrees b.
110 degrees plus m angle 4 equals 180 degrees Substitution Property
m angle 4 equals 70 degrees Subtraction Property of Equality
m angle D equals m angle 4 Definition of angle D
m angle D equals 70 degrees Substitution Property