Warm ups Choose the plane parallel to plane MNR. Choose the segment skew to MP. Classify the relationship between <1 and <5. Classify the relationship.

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Presentation transcript:

Warm ups Choose the plane parallel to plane MNR. Choose the segment skew to MP. Classify the relationship between <1 and <5. Classify the relationship between <3 and <8. Classify the relationship between <4 and <6.

3-2 ANGLES AND PARALLEL LINES

Corresponding Angles Postulate If 2 parallel lines are cut by a transversal, then corresponding angles are congruent. (Corr. Ang. Post) What 4 pairs are congruent? <1 & <5, <2 & <6, <3 & <7 and <4 & <

Example In the figure, m<11 = 51. Find m<15. Tell which postulates (or theorems) you used. Answer: m<15 = 51 <15 is congruent to <11: Corr. Ang. Postulate

Example 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<11Corr. Ang. Post. <16<11Transitive Property

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

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

Alternate Interior Angles Theorem If 2 parallels are cut by a transversal, then alternate interior angles are congruent. (Alt. Int. Thm) What 2 pairs of angles are congruent? <3 & <6, <4 & <

Consecutive Interior Angles Thm If two parallels are cut by a transversal, then consec. interior angles are supplements. (CIA Thm) CIA are the only one that is SUPPS!! (Bracket) What 2 pairs are supps? <3 + <5 = 180, <4 + <6 =

Alternate Ext. Angles Theorem If 2 parallels are cut by a transversal, then alternate exterior angles are congruent. (Alt. ext. Thm) What 2 pairs of angles are congruent? <1 & <8, <2 & <

Example 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 Answer: m<3 = 125

Example 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.

ALGEBRA If m<5 = 2x – 10, and m<7 = x + 15, find x. Example <5 <7 Corresponding Angles Postulate 2x – 10 =x + 15 x – 10 =15 x =25Answer: x = 25

If m<4 = 4(y – 25), and m<8 = 4y, find y. Example (watch the WB if you get lost) <8 <6Corr. Ang. Post. m<6 + m<4=180Supplement Theorem 4y + 4(y – 25)=180 4y + 4y – 100=180 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 and y. TWAP!!!!! Think!!! A.x = 9, y =14 B.x = 12, y = 20 C.x = 12, y = 14 D.x = 14, y = 12

Perp. Transversal Thm. If a transversal is perp. to one of two parallel lines, then it is perp. to the other line as well.

Homework Pg. 183 # 11 – 19, 25, 27, 29, 36, 43, 46