University:
High School
Course:
High School Geometry
Academic year:

2022
Views:

84

Pages:

11
Author:

efreet4ifh37v

LESSON 3-3 Proofs with parallel lines Learning Target 3.2 I can describe, draw and write a two-column proof involving angle relationships of parallel lines cut by a transversal. The converses of the 4 properties of angle relationships between parallel lines and a traversal are also true: If lines l and m are parallel, then corresponding angles and congruent. If corresponding angles are congruent, then lines l and m are parallel. If lines a and b are parallel, then alternate interior angles are congruent. If alternate interior angles are congruent, then lines a and b are parallel. If lines a and b are parallel, then alternate exterior angles are congruent. If alternate exterior angles are congruent then lines a and b are parallel. If lines a and b are parallel, then consecutive interior angles are supplementary. If consecutive interior angles are supplementary, then lines a and b are parallel. Example 1 Use the diagram above. Which lines, if any, must be parallel if 3 and 2 are supplementary? It is given that 3 and 2 are supplementary. Angle 2 + angle 3 = 180 Given Angle 2 + angle 4 = 180 by angle addition post. Angle 3 = angle 4 by substitution and subtraction Angle 3 and angle 4 are corresponding. EC || DK by the converse of the Corresponding angles theorem. Example 2 Find the value of x for which || m. The labeled angles are alternate interior angles. Since || m, the alternate interior angles are congruent. Write and solve the equation 5x – 66 = 14 + 3x. 5x = 80 + 3x Add 66 to each side. 2x = 80 Subtract 3x from each side. x = 40 Divide each side by 2. You Try #1 Use the diagram above. Which lines, if any, must be parallel if are congruent? Explain. A. B. C. D. 3 and 4 EC ll DK, by the Converse of Corresponding Angles Postulate. EC ll DK, by the Converse of the consecutive Interior Angles Theorem. ED ll CK, by the Converse of Corresponding Angles Postulate ED ll CK, by the Converse of consecutive Interior Angles Theorem. The answer is A. You Try #2 Find the value of x for which 7 x − 8 + 62 = 180 7 x + 54 = 180 7 x = 126 x = 18 allb Lines in the Coordinate Plane Example 3 Use the slope and y-intercept to graph the line y = –2x + 9 and y=-2x+3. When an equation is written in the form y = mx + b, m is the slope and b is the y-intercept. In the equation y = –2x + 9, the slope is –2 and the y-intercept is 9. You Try #3 Use the slope and y-intercept to graph the line y = –3x + 3 and y=3x-3. Example 4 Give the missing reasons in this proof of the Corresponding Angles Postulate. Given: allb Prove: ∠1 ≅ ∠2 Statements: allb 2. ∠2 ≅ ∠4 3. ∠4 ≅ ∠1 4. ∠1 ≅ ∠2 1. Reasons: 1. Given 2. Vertical angles theorem 3. Alternate exterior angles are congruent 4. Transitive You Try #4 A 2. 3. B 2. 3. C 2. 3. Vertical angles are congruent. Corresponding angles are congruent. Same side interior angles are congruent. Vertical angles are congruent. Corresponding angles are congruent. Vertical angles are congruent.