Splash Screen
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