Unit Three: More Proofs for Postulates 9 and 10

Match the reasons with the statements in the proof to prove that lines l and m are parallel, given that m∠2 = 122° and m∠3 = 58° Given: measure of angle 2 = 122° measure of angle 3 = 58° Prove: l || m STATEMENT: 1. m∠2 = 122° and m∠3 = 58° 2. ∠3 and ∠5 are supplementary angles 3. m∠3 + m∠5 = 180° 4. 58° + m∠5 = 180° 5. m∠5 = 122° 6. m∠2 = m∠5 7. l || m

1. Given 2. Exterior Sides in Opposite Rays 3. Definition of Supplementary Angles 4. Substitution 5. Subtraction Property of Equality 6. Substitution 7. If corresponding angles are equal, then lines are parallel

Match the reasons with the statements in the proof. Given: j || k m∠1 = m∠3 Prove: l || m STATEMENT: 1. j || k, m∠3 = m∠1 2. m∠1 = m∠2 3. m∠2 = m∠3 4. l || m REASONS: Substitution If alternate interior angles are =, then lines are ||. Given If lines are ||, then corresponding angles are =.

1. Given 2. If lines are ||, then corresponding angles are =. 3. If alternate interior angles are =, then lines are ||. 4. Substitution

Match the reasons with the statements in the proof. Given: m∠6 = m∠8 b | | c Prove: a || b STATEMENT: 1. m∠6 = m∠8, b||c 2. m∠7 = m∠8 3. m∠6 = m∠7 4. a||b REASONS: If alternate interior angles equal, then lines ||. Substitution If lines ||, corresponding angles =. Given

1. Given 2. If lines ||, corresponding angles =. 3. If alternate interior angles equal, then lines ||. 4. Substitution

Match the reasons to the statements in the proof. Given: m∠1 + m∠5 = 180° m∠1 + m∠4 = 180° Prove: Ray YZ || Ray UV STATEMENT: 1. m∠1 + m∠5 = 180° and m∠1 + m∠4=180° 2. m∠1 + m∠5 = m∠1 + m∠4 3. m∠5 = m∠4 4. Ray YZ is parallel to Ray UV REASONS: Subtraction property of equality Substitution If alternate interior angles equal, then lines are ||. Given

1. Given 2. Substitution 3. Subtraction property of equality 4. If alternate interior angles equal, then lines are ||.

Given: ∠A, ∠B, ∠C, ∠D are rt. ∠'s Prove: Segment AD || Segment BC Segment AB || Segment DC Which of the following reasons could be used to conclude that the lines are parallel based on the given information? If right angles are formed, then lines are parallel. If two lines are perpendicular to another line, then they are parallel. If alternate interior angles are equal, then lines are parallel.

If two lines are perpendicular to another line, then they are parallel.

In a word processing document or on a separate piece of paper, use the guide to construct a two column proof proving that lines l and m are parallel. Angles 1 and 2 are supplementary by definition. Submit the entire proof to your instructor. Given: ∠1 and ∠2 are supplementary angles Prove: l || m STATEMENT: 1.∠1 and ∠2 are supplementary angles 2. m∠1 + m∠2 = 180° 3. ∠1 and ∠3 are supplementary angles 4. ___ 5. m∠1 + m∠2 = m∠1 + m∠3 6. ___ 7. l || m REASON: 1. Given 2. ___ 3. Exterior sides in opposite rays 4. ___ 5. ___ 6. ___ 7. ___

STATEMENT: 4. measure of angle 1 + measure of angle 2 = 180 degrees 6. measure of angle 2 = measure of angle 3 REASON: 2. definition of supplementary angles 4. definition of supplementary angles 5. substitution 6. subtraction 7. If two lines are cut by a transversal so alternate interior angles are equal, then the lines are parallel (theorem 3-15)

True/False - Use the following figure to answer the question. If angle 1 and angle 2 are equal, then lines l and m are parallel.

True

True/False - Use the following figure to answer the question. If line t is perpendicular to both line l and line m, then angle 1 and angle 2 are both right angles.

True

True/False - Use the following figure to answer the question. If lines l and m are parallel, then angle 2 and angle 3 are corresponding angles.

True

True/False - Use the following figure to answer the question. When line t is perpendicular to both line l and line m, then lines l and m are parallel.

True