3 3 Proving Lines Parallel Warm Up Lesson

3 -3 Proving Lines Parallel Objective Use the angles formed by a transversal to

3 -3 Proving Lines Parallel Holt Mc. Dougal Geometry

3 -3 Proving Lines Parallel Example 1 A: Using the Converse of the Corresponding

3 -3 Proving Lines Parallel Example 1 B: Using the Converse of the Corresponding

3 -3 Proving Lines Parallel Example 2 A: Determining Whether Lines are Parallel Use

3 -3 Proving Lines Parallel Example 2 B Continued Use the given information and

3 -3 Proving Lines Parallel Example 3: Proving Lines Parallel Given: p || r

3 -3 Proving Lines Parallel Example 3 Continued Statements Reasons 1. p || r

3 -3 Proving Lines Parallel Example 4: Carpentry Application A carpenter is creating a

3 -3 Proving Lines Parallel Example 4 Continued A line through the center of

3 -3 Proving Lines Parallel Example 4 Continued m 1 = 8 x +

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3 -3 Proving. Lines. Parallel Warm Up Lesson Presentation Lesson Quiz Holt Geometry Holt Mc. Dougal Geometry

3 -3 Proving Lines Parallel Objective Use the angles formed by a transversal to prove two lines are parallel. Holt Mc. Dougal Geometry

3 -3 Proving Lines Parallel Holt Mc. Dougal Geometry

3 -3 Proving Lines Parallel Example 1 A: Using the Converse of the Corresponding Angles Postulate Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m. 4 8 ℓ || m Holt Mc. Dougal Geometry 4 and 8 are corresponding angles. Conv. of Corr. s Post.

3 -3 Proving Lines Parallel Example 1 B: Using the Converse of the Corresponding Angles Postulate Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m. m 3 = (4 x – 80)°, m 7 = (3 x – 50)°, x = 30 m 3 = 4(30) – 80 = 40 m 8 = 3(30) – 50 = 40 m 3 = m 8 3 8 ℓ || m Holt Mc. Dougal Geometry Substitute 30 for x. Trans. Prop. of Equality Def. of s. Conv. of Corr. s Post.

3 -3 Proving Lines Parallel Example 2 A: Determining Whether Lines are Parallel Use the given information and theorems you have learned to show that r || s. 4 8 4 and 8 are alternate exterior angles. r || s Conv. Of Alt. Int. s Thm. Holt Mc. Dougal Geometry

3 -3 Proving Lines Parallel Example 2 B Continued Use the given information and theorems you have learned to show that r || s. m 2 = (10 x + 8)°, m 3 = (25 x – 3)°, x = 5 m 2 + m 3 = 58° + 122° = 180° r || s Holt Mc. Dougal Geometry 2 and 3 are same-side interior angles. Conv. of Same-Side Int. s Thm.

3 -3 Proving Lines Parallel Example 3: Proving Lines Parallel Given: p || r , 1 3 Prove: ℓ || m Holt Mc. Dougal Geometry

3 -3 Proving Lines Parallel Example 3 Continued Statements Reasons 1. p || r 1. Given 2. 3 2 2. Alt. Ext. s Thm. 3. 1 3 3. Given 4. 1 2 4. Trans. Prop. of 5. ℓ ||m 5. Conv. of Corr. s Post. Holt Mc. Dougal Geometry

3 -3 Proving Lines Parallel Example 4: Carpentry Application A carpenter is creating a woodwork pattern and wants two long pieces to be parallel. m 1= (8 x + 20)° and m 2 = (2 x + 10)°. If x = 15, show that pieces A and B are parallel. Holt Mc. Dougal Geometry

3 -3 Proving Lines Parallel Example 4 Continued A line through the center of the horizontal piece forms a transversal to pieces A and B. 1 and 2 are same-side interior angles. If 1 and 2 are supplementary, then pieces A and B are parallel. Substitute 15 for x in each expression. Holt Mc. Dougal Geometry

3 -3 Proving Lines Parallel Example 4 Continued m 1 = 8 x + 20 = 8(15) + 20 = 140 Substitute 15 for x. m 2 = 2 x + 10 = 2(15) + 10 = 40 m 1+m 2 = 140 + 40 = 180 Substitute 15 for x. 1 and 2 are supplementary. The same-side interior angles are supplementary, so pieces A and B are parallel by the Converse of the Same-Side Interior Angles Theorem. Holt Mc. Dougal Geometry