1 / 22

1-1a

(over Lesson 3-5). 1-1a. Slide 1 of 1. (over Lesson 3-5). 1-1b. Slide 1 of 1. §3.6 Congruent Angles. What You'll Learn. You will learn to identify and use congruent and vertical angles. Recall that congruent segments have the same ________. measure. Congruent angles.

keaton-mcintyre
Download Presentation

1-1a

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. (over Lesson 3-5) 1-1a Slide 1 of 1

  2. (over Lesson 3-5) 1-1b Slide 1 of 1

  3. §3.6 Congruent Angles What You'll Learn You will learn to identify and use congruent and vertical angles. Recall that congruent segments have the same ________. measure Congruent angles _______________ also have the same measure.

  4. 50° 50° B V §3.6 Congruent Angles Two angles are congruent iff, they have the same ______________. degree measure B  V iff mB = mV

  5. 1 2 X Z §3.6 Congruent Angles arcs To show that 1 is congruent to 2, we use ____. To show that there is a second set of congruent angles, X and Z, we use double arcs. This “arc” notation states that: X  Z mX = mZ

  6. §3.6 Congruent Angles four When two lines intersect, ____ angles are formed. There are two pair of nonadjacent angles. vertical angles These pairs are called _____________. 1 4 2 3

  7. §3.6 Congruent Angles Two angles are vertical iff they are two nonadjacent angles formed by a pair of intersecting lines. Vertical angles: 1 and 3 1 4 2 2 and 4 3

  8. 1 4 2 3 §3.6 Congruent Angles 1) On a sheet of paper, construct two intersecting lines that are not perpendicular. 2) With a protractor, measure each angle formed. 3) Make a conjecture about vertical angles. Consider: A. 1 is supplementary to 4. m1 + m4 = 180 Hands-On B. 3 is supplementary to 4. m3 + m4 = 180 Therefore, it can be shown that 1 3 Likewise, it can be shown that 24

  9. 1 4 2 3 §3.6 Congruent Angles 1) If m1 = 4x + 3 and the m3 = 2x + 11, then find the m3 x = 4; 3 = 19° 2) If m2 = x + 9 and the m3 = 2x + 3, then find the m4 x = 56; 4 = 65° 3) If m2 = 6x - 1 and the m4 = 4x + 17, then find the m3 x = 9; 3 = 127° 4) If m1 = 9x - 7 and the m3 = 6x + 23, then find the m4 x = 10; 4 = 97°

  10. §3.6 Congruent Angles Vertical angles are congruent. n m 2 1  3 3 1 2  4 4

  11. 130° x° §3.6 Congruent Angles Find the value of x in the figure: The angles are vertical angles. So, the value of x is 130°.

  12. §3.6 Congruent Angles Find the value of x in the figure: The angles are vertical angles. (x – 10) = 125. (x – 10)° x – 10 = 125. 125° x = 135.

  13. §3.6 Congruent Angles Suppose two angles are congruent. What do you think is true about their complements? 1  2 2 + y = 90 1 + x = 90 y is the complement of 2 x is the complement of 1 y = 90 - 2 x = 90 - 1 Because 1  2, a “substitution” is made. y = 90 - 1 x = 90 - 1 x = y x  y If two angles are congruent, their complements are congruent.

  14. 60° 60° B A 1 2 3 4 §3.6 Congruent Angles If two angles are congruent, then their complements are _________. congruent The measure of angles complementary to A and B is 30. A  B If two angles are congruent, then their supplements are _________. congruent The measure of angles supplementary to 1 and 4 is 110. 110° 110° 70° 70° 4  1

  15. 3 1 2 §3.6 Congruent Angles If two angles are complementary to the same angle, then they are _________. congruent 3 is complementary to 4 5 is complementary to 4 4 3 5 5  3 If two angles are supplementary to the same angle, then they are _________. congruent 1 is supplementary to 2 3 is supplementary to 2 1  3

  16. 52° 52° A B §3.6 Congruent Angles Suppose A  B and mA = 52. Find the measure of an angle that is supplementary to B. 1 B + 1 = 180 1 = 180 – B 1 = 180 – 52 1 = 128°

  17. §3.6 Congruent Angles If 1 is complementary to 3, 2 is complementary to 3, and m3 = 25, What are m1 and m2 ? m1 + m3 = 90 Definition of complementary angles. m1 = 90 - m3 Subtract m3 from both sides. m1 = 90 - 25Substitute 25 in for m3. m1 = 65Simplify the right side. You solve for m2 m2 + m3 = 90 Definition of complementary angles. m2 = 90 - m3 Subtract m3 from both sides. m2 = 90 - 25Substitute 25 in for m3. m2 = 65Simplify the right side.

  18. G D 1 2 A C 4 B 3 E H §3.6 Congruent Angles 1) If m1 = 2x + 3 and the m3 = 3x - 14, then find the m3 x = 17; 3 = 37° 2) If mABD = 4x + 5 and the mDBC = 2x + 1, then find the mEBC x = 29; EBC = 121° 3) If m1 = 4x - 13 and the m3 = 2x + 19, then find the m4 x = 16; 4 = 39° 4) If mEBG = 7x + 11 and the mEBH = 2x + 7, then find the m1 x = 18; 1 = 43°

  19. Suppose you draw two angles that are congruent and supplementary. What is true about the angles?

  20. 1 2 C A B §3.6 Congruent Angles If two angles are congruent and supplementary then each is a __________. right angle 1 is supplementary to 2 1 and 2 = 90 All right angles are _________. congruent A  B  C

  21. B A 2 E 3 1 4 C D §3.6 Congruent Angles If 1 is supplementary to 4, 3 is supplementary to 4, and m 1 = 64, what are m 3 and m 4? They are vertical angles. 1  3 m 1 = m3 m 3 = 64 3 is supplementary to 4 Given Definition of supplementary. m3 + m4 = 180 64 + m4 = 180 m4 = 180 – 64 m4 = 116

  22. End of Lesson

More Related