Lesson 3 2 Angles and Parallel Lines Transparency
![Lesson 3 -2 Angles and Parallel Lines Lesson 3 -2 Angles and Parallel Lines](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-1.jpg)
![Transparency 3 -2 5 -Minute Check on Lesson 3 -1 Refer to the figure. Transparency 3 -2 5 -Minute Check on Lesson 3 -1 Refer to the figure.](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-2.jpg)
![Transparency 3 -2 5 -Minute Check on Lesson 3 -1 Refer to the figure. Transparency 3 -2 5 -Minute Check on Lesson 3 -1 Refer to the figure.](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-3.jpg)
![Objectives • Use the properties of parallel lines to determine congruent angles • Use Objectives • Use the properties of parallel lines to determine congruent angles • Use](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-4.jpg)
![Vocabulary • No new vocabulary words or symbols Vocabulary • No new vocabulary words or symbols](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-5.jpg)
![t Parallel Lines and Transversals Postulate/ Theorem k 3 l 5 7 1 2 t Parallel Lines and Transversals Postulate/ Theorem k 3 l 5 7 1 2](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-6.jpg)
![In the figure x || y and m 11 = 51. Find m 16. In the figure x || y and m 11 = 51. Find m 16.](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-7.jpg)
![In the figure, a || b and m 18 = 42. Find m 19 In the figure, a || b and m 18 = 42. Find m 19](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-8.jpg)
![What is the measure of RTV? You need to find RTV. Be sure to What is the measure of RTV? You need to find RTV. Be sure to](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-9.jpg)
![Solve the Test Item Alternate Interior Angles Theorem Definition of congruent angles Substitution Angle Solve the Test Item Alternate Interior Angles Theorem Definition of congruent angles Substitution Angle](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-10.jpg)
![What is the measure of IGE? Answer: 93 What is the measure of IGE? Answer: 93](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-11.jpg)
![ALGEBRA If and find x and y. Find x. by the Corresponding Angles Postulate. ALGEBRA If and find x and y. Find x. by the Corresponding Angles Postulate.](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-12.jpg)
![Find y. by the Alternate Exterior Angles Theorem. Definition of congruent angles Substitution Simplify. Find y. by the Alternate Exterior Angles Theorem. Definition of congruent angles Substitution Simplify.](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-13.jpg)
![ALGEBRA: If m 1 = 9 x + 6, m 2 = 2(5 x ALGEBRA: If m 1 = 9 x + 6, m 2 = 2(5 x](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-14.jpg)
![Decision Tree for Special Pairs no ye s b int oth er ior Are Decision Tree for Special Pairs no ye s b int oth er ior Are](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-15.jpg)
![Identification: Determine what each of these angle pairs are in the drawing below: Acute Identification: Determine what each of these angle pairs are in the drawing below: Acute](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-16.jpg)
![ALGEBRA: If m 4 = 2 x + 16 and m 4 = 2(4 ALGEBRA: If m 4 = 2 x + 16 and m 4 = 2(4](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-17.jpg)
![ALGEBRA: If m 1 = 9 x + 6, m 2 = 2(5 x ALGEBRA: If m 1 = 9 x + 6, m 2 = 2(5 x](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-18.jpg)
![Summary & Homework • Summary: – Pairs of congruent angles formed by parallel lines Summary & Homework • Summary: – Pairs of congruent angles formed by parallel lines](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-19.jpg)
- Slides: 19
![Lesson 3 2 Angles and Parallel Lines Lesson 3 -2 Angles and Parallel Lines](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-1.jpg)
Lesson 3 -2 Angles and Parallel Lines
![Transparency 3 2 5 Minute Check on Lesson 3 1 Refer to the figure Transparency 3 -2 5 -Minute Check on Lesson 3 -1 Refer to the figure.](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-2.jpg)
Transparency 3 -2 5 -Minute Check on Lesson 3 -1 Refer to the figure. 1. Name all planes parallel to MNR. 2. Name all segments skew to MP. Give the special name for each angle pair in the figure. 3. 1 and 5 4. 3 and 8 5. 4 and 6 6. How many pairs of alternate interior angles are there in the figure above? Standardized Test Practice: A 1 B 2 C 3 D 4
![Transparency 3 2 5 Minute Check on Lesson 3 1 Refer to the figure Transparency 3 -2 5 -Minute Check on Lesson 3 -1 Refer to the figure.](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-3.jpg)
Transparency 3 -2 5 -Minute Check on Lesson 3 -1 Refer to the figure. 1. Name all planes parallel to MNR. Plane POS (can be named with any 3 letters from POST) 2. Name all segments skew to MP. TS, QR, NR, OS Give the special name for each angle pair in the figure. 3. 1 and 5 corresponding angles 4. 3 and 8 consecutive interior angles 5. 4 and 6 alternate exterior angles 6. How many pairs of alternate interior angles are there in the figure above? Standardized Test Practice: A 1 B 2 C 3 D 4
![Objectives Use the properties of parallel lines to determine congruent angles Use Objectives • Use the properties of parallel lines to determine congruent angles • Use](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-4.jpg)
Objectives • Use the properties of parallel lines to determine congruent angles • Use algebra to find angle measures
![Vocabulary No new vocabulary words or symbols Vocabulary • No new vocabulary words or symbols](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-5.jpg)
Vocabulary • No new vocabulary words or symbols
![t Parallel Lines and Transversals Postulate Theorem k 3 l 5 7 1 2 t Parallel Lines and Transversals Postulate/ Theorem k 3 l 5 7 1 2](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-6.jpg)
t Parallel Lines and Transversals Postulate/ Theorem k 3 l 5 7 1 2 4 6 8 Statement If two parallel lines are cut by a transversal, Examples 1 5, 2 6, 3 7, 4 8 Corresponding Angles Post. then each pair of corresponding angles is congruent Alternate Interior Angles Thrm then each pair of alternate interior angles is 3 6, 4 5 congruent Consecutive Interior Angles Thrm then each pair of consecutive interior angles is supplementary m 3 + m 5 = 180°, m 4 + m 6 = 180° Alternate Exterior Angles Thrm then each pair of alternate exterior angles is congruent 1 8, 2 7 Perpendicular Transversal Thrm In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other. None illustrated
![In the figure x y and m 11 51 Find m 16 In the figure x || y and m 11 = 51. Find m 16.](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-7.jpg)
In the figure x || y and m 11 = 51. Find m 16. Corresponding Angles Postulate Vertical Angles Theorem Transitive Property Definition of congruent angles Substitution Answer:
![In the figure a b and m 18 42 Find m 19 In the figure, a || b and m 18 = 42. Find m 19](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-8.jpg)
In the figure, a || b and m 18 = 42. Find m 19 and m 25 Answer: m 19 = 138 , and m 25 = 42
![What is the measure of RTV You need to find RTV Be sure to What is the measure of RTV? You need to find RTV. Be sure to](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-9.jpg)
What is the measure of RTV? You need to find RTV. Be sure to identify it correctly on the figure. Look for patterns!!
![Solve the Test Item Alternate Interior Angles Theorem Definition of congruent angles Substitution Angle Solve the Test Item Alternate Interior Angles Theorem Definition of congruent angles Substitution Angle](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-10.jpg)
Solve the Test Item Alternate Interior Angles Theorem Definition of congruent angles Substitution Angle Addition Postulate
![What is the measure of IGE Answer 93 What is the measure of IGE? Answer: 93](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-11.jpg)
What is the measure of IGE? Answer: 93
![ALGEBRA If and find x and y Find x by the Corresponding Angles Postulate ALGEBRA If and find x and y. Find x. by the Corresponding Angles Postulate.](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-12.jpg)
ALGEBRA If and find x and y. Find x. by the Corresponding Angles Postulate. Definition of congruent angles Substitution Subtract x from each side and add 10 to each side.
![Find y by the Alternate Exterior Angles Theorem Definition of congruent angles Substitution Simplify Find y. by the Alternate Exterior Angles Theorem. Definition of congruent angles Substitution Simplify.](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-13.jpg)
Find y. by the Alternate Exterior Angles Theorem. Definition of congruent angles Substitution Simplify. Add 100 to each side. Divide each side by 4. Answer:
![ALGEBRA If m 1 9 x 6 m 2 25 x ALGEBRA: If m 1 = 9 x + 6, m 2 = 2(5 x](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-14.jpg)
ALGEBRA: If m 1 = 9 x + 6, m 2 = 2(5 x – 3), and m 3 = 5 y + 14, find x and y. Answer: x = 12 and y = 20
![Decision Tree for Special Pairs no ye s b int oth er ior Are Decision Tree for Special Pairs no ye s b int oth er ior Are](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-15.jpg)
Decision Tree for Special Pairs no ye s b int oth er ior Are they on opposite sides of transversal Where are the two angles? one of each Are they on opposite sides of transversal no ye s th bo rior te ex Are they on opposite sides of transversal no ye s Consecutive Int Alt Interior Corresponding None Alt Exterior
![Identification Determine what each of these angle pairs are in the drawing below Acute Identification: Determine what each of these angle pairs are in the drawing below: Acute](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-16.jpg)
Identification: Determine what each of these angle pairs are in the drawing below: Acute Angle: Alternate Interior Angles: 9 5 11 13 14 8 6 12 10 4 16 15 7 Alternate Exterior Angles: Corresponding Angles: Consecutive Interior Angles: Linear Pair of Angles: Obtuse Angle: Right Angle: Vertical Angle Pair: Answer: many combinations are possible
![ALGEBRA If m 4 2 x 16 and m 4 24 ALGEBRA: If m 4 = 2 x + 16 and m 4 = 2(4](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-17.jpg)
ALGEBRA: If m 4 = 2 x + 16 and m 4 = 2(4 x – 3), find m 1, and m 4. 4 Answer: m 1 = 130° m 4 = 50°.
![ALGEBRA If m 1 9 x 6 m 2 25 x ALGEBRA: If m 1 = 9 x + 6, m 2 = 2(5 x](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-18.jpg)
ALGEBRA: If m 1 = 9 x + 6, m 2 = 2(5 x – 3), and m 3 = 5 y + 14, find m 1, m 2, m 3, and m 4. 4 Answer: m 1 = 114°, m 2 = 114°, m 3 = 114°, and m 4 = 66°.
![Summary Homework Summary Pairs of congruent angles formed by parallel lines Summary & Homework • Summary: – Pairs of congruent angles formed by parallel lines](https://slidetodoc.com/presentation_image_h/34b42d07c5488d777f6b78a5e941eefa/image-19.jpg)
Summary & Homework • Summary: – Pairs of congruent angles formed by parallel lines and a transversal are corresponding angles, alternate interior angles and alternate exterior angles – Pairs of consecutive interior angles are supplementary • Homework: – Day 1: pg 136 – 137: 1, 5 -11, 14 -19 – Day 2: pg 136 – 137: 20 -25, 26, 27, 29, 31, 39
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