Splash Screen. Lesson Menu Five-Minute Check (over Lesson 3–1) CCSS Then/Now Postulate 3.1:Corresponding Angles Postulate Example 1:Use Corresponding.

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Presentation transcript:

Splash Screen

Lesson Menu Five-Minute Check (over Lesson 3–1) CCSS Then/Now Postulate 3.1:Corresponding Angles Postulate Example 1:Use Corresponding Angles Postulate Theorems:Parallel Lines and Angle Pairs Proof: Alternate Interior Angles Theorem Example 2:Real-World Example: Use Theorems about Parallel Lines Example 3:Find Values of Variables Theorem 3.4: Perpendicular Transversal Theorem

Over Lesson 3–1 5-Minute Check 1 A.RST B.PON C.STQ D.POS Choose the plane parallel to plane MNR.

Over Lesson 3–1 5-Minute Check 1 A.RST B.PON C.STQ D.POS Choose the plane parallel to plane MNR.

Over Lesson 3–1 5-Minute Check 2 A.PM B.TS C.PO D.MQ ___ Choose the segment skew to MP.

Over Lesson 3–1 5-Minute Check 2 A.PM B.TS C.PO D.MQ ___ Choose the segment skew to MP.

Over Lesson 3–1 5-Minute Check 3 A.corresponding angles B.vertical angles C.consecutive interior angles D. alternate exterior angles Classify the relationship between  1 and  5.

Over Lesson 3–1 5-Minute Check 3 A.corresponding angles B.vertical angles C.consecutive interior angles D. alternate exterior angles Classify the relationship between  1 and  5.

Over Lesson 3–1 5-Minute Check 4 A.alternate interior angles B.alternate exterior angles C.corresponding angles D.consecutive interior angles Classify the relationship between  3 and  8.

Over Lesson 3–1 5-Minute Check 4 A.alternate interior angles B.alternate exterior angles C.corresponding angles D.consecutive interior angles Classify the relationship between  3 and  8.

Over Lesson 3–1 5-Minute Check 5 A.alternate interior angles B.alternate exterior angles C.corresponding angles D.vertical angles Classify the relationship between  4 and  6.

Over Lesson 3–1 5-Minute Check 5 A.alternate interior angles B.alternate exterior angles C.corresponding angles D.vertical angles Classify the relationship between  4 and  6.

Over Lesson 3–1 A.OS B.TS C.NR D.MQ 5-Minute Check 6 Which of the following segments is not parallel to PT?

Over Lesson 3–1 A.OS B.TS C.NR D.MQ 5-Minute Check 6 Which of the following segments is not parallel to PT?

CCSS Content Standards G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G.CO.9 Prove theorems about lines and angles. Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others.

Then/Now You named angle pairs formed by parallel lines and transversals. Use theorems to determine the relationships between specific pairs of angles. Use algebra to find angle measurements.

Concept

Example 1 Use Corresponding Angles Postulate A. In the figure, m  11 = 51. Find m  15. Tell which postulates (or theorems) you used. Answer:  15  11 Corresponding Angles Postulate m  15 = m  11 Definition of congruent angles m  15 = 51 Substitution

Example 1 Use Corresponding Angles Postulate A. In the figure, m  11 = 51. Find m  15. Tell which postulates (or theorems) you used. Answer: m  15 = 51  15  11 Corresponding Angles Postulate m  15 = m  11 Definition of congruent angles m  15 = 51 Substitution

Example 1 Use Corresponding Angles Postulate B. In the figure, m  11 = 51. Find m  16. Tell which postulates (or theorems) you used. Answer:  16  15Vertical Angles Theorem  15  11Corresponding Angles Postulate  16  11Transitive Property (  ) m  16=m  11Definition of congruent angles m  16=51Substitution

Example 1 Use Corresponding Angles Postulate B. In the figure, m  11 = 51. Find m  16. Tell which postulates (or theorems) you used. Answer: m  16 = 51  16  15Vertical Angles Theorem  15  11Corresponding Angles Postulate  16  11Transitive Property (  ) m  16=m  11Definition of congruent angles m  16=51Substitution

Example 1a A.42 B.84 C.48 D.138 A. In the figure, a || b and m  18 = 42. Find m  22.

Example 1a A.42 B.84 C.48 D.138 A. In the figure, a || b and m  18 = 42. Find m  22.

Example 1b A.42 B.84 C.48 D.138 B. In the figure, a || b and m  18 = 42. Find m  25.

Example 1b A.42 B.84 C.48 D.138 B. In the figure, a || b and m  18 = 42. Find m  25.

Concept

Example 2 Use Theorems about Parallel Lines FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m  2 = 125, find m  3.  2  3 Alternate Interior Angles Theorem m  2 = m  3 Definition of congruent angles 125 = m  3 Substitution Answer:

Example 2 Use Theorems about Parallel Lines FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m  2 = 125, find m  3.  2  3 Alternate Interior Angles Theorem m  2 = m  3 Definition of congruent angles 125 = m  3 Substitution Answer: m  3 = 125

Example 2 A.25 B.55 C.70 D.125 FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m  2 = 125, find m  4.

Example 2 A.25 B.55 C.70 D.125 FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m  2 = 125, find m  4.

A. ALGEBRA If m  5 = 2x – 10, and m  7 = x + 15, find x. Example 3 Find Values of Variables  5  7 Corresponding Angles Postulate m  5 = m  7 Definition of congruent angles 2x – 10 = x + 15 Substitution x – 10 =15Subtract x from each side. x =25Add 10 to each side. Answer:

A. ALGEBRA If m  5 = 2x – 10, and m  7 = x + 15, find x. Example 3 Find Values of Variables  5  7 Corresponding Angles Postulate m  5 = m  7 Definition of congruent angles 2x – 10 = x + 15 Substitution x – 10 =15Subtract x from each side. x =25Add 10 to each side. Answer: x = 25

B. ALGEBRA If m  4 = 4(y – 25), and m  8 = 4y, find y. Example 3 Find Values of Variables  8  6Corresponding Angles Postulate m  8=m  6Definition of congruent angles 4y=m  6Substitution

Example 3 Find Values of Variables m  6 + m  4=180Supplement Theorem 4y + 4(y – 25)=180Substitution 4y + 4y – 100=180Distributive Property 8y=280Add 100 to each side. y=35Divide each side by 8. Answer:

Example 3 Find Values of Variables m  6 + m  4=180Supplement Theorem 4y + 4(y – 25)=180Substitution 4y + 4y – 100=180Distributive Property 8y=280Add 100 to each side. y=35Divide each side by 8. Answer: y = 35

A. ALGEBRA If m  1 = 9x + 6, m  2 = 2(5x – 3), and m  3 = 5y + 14, find x. Example 3 A.x = 9 B.x = 12 C.x = 10 D.x = 14

A. ALGEBRA If m  1 = 9x + 6, m  2 = 2(5x – 3), and m  3 = 5y + 14, find x. Example 3 A.x = 9 B.x = 12 C.x = 10 D.x = 14

B. ALGEBRA If m  1 = 9x + 6, m  2 = 2(5x – 3), and m  3 = 5y + 14, find y. Example 3 A.y = 14 B.y = 20 C.y = 16 D.y = 24

B. ALGEBRA If m  1 = 9x + 6, m  2 = 2(5x – 3), and m  3 = 5y + 14, find y. Example 3 A.y = 14 B.y = 20 C.y = 16 D.y = 24

Concept

End of the Lesson