1 / 16

Chapter 5 Section 3

Chapter 5 Section 3. Theorems Involving Parallel Lines. Warm-Up: Thursday, March 27 th. Part 1: Parallelograms Methods of Proof . Part 2: Algebraic Connections What values must x and y have to make the quadrilateral a parallelogram.

plato
Télécharger la présentation

Chapter 5 Section 3

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. Chapter 5 Section 3 Theorems Involving Parallel Lines

  2. Warm-Up: Thursday, March 27th Part 1: Parallelograms Methods of Proof Part 2: Algebraic Connections What values must x and y have to make the quadrilateral a parallelogram • State the 4 ways to prove a quadrilateral is a parallelogram. 8x - 6 3y 42

  3. 1.) Definition of parallelogram 2.) Both pairs of opposite sides  3.) One pair of sides both || and  4.) Diagonals bisect each other 5.) Both pairs of opposite angles  6.) Answers vary 7.) Diagonals bisect each other 14.) See next slide 19.) x =18, y=14 20.) x=20, y=6 or -5 21.) x=10, y=2 22.) x=11, y=5 p. 174 #’s 1 – 7, 14, 19 -22 Homework: Wednesday, April 2

  4. 14.) Given: Parallelogram ABCD M and N are midpoints of AB and DC Prove: AMCN is a parallelogram D N C A M B

  5. Parallel Lines…What do you know? You should know lots… I hope 

  6. Tell me EVERYTING You know about… Parallel Lines Parallelograms

  7. Theorem 5.9: • If parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal. (not just limited to 3 lines) Given: AX || BY||CZ AB  BC Prove: XY  YZ A X B Y C Z

  8. Application of Theorem 5.9 • Given: AR||BS||CT; RS  ST • RS = 12, ST = • AB = 8; BC = • AC = 20; AB = • AC = 10x; BC = A R B S C T

  9. Theorem 5.10: • A line that contains the midpoint of one side of a triangle and is parallel to another side passes through the midpoint of the third side. A Given: M is the midpoint of AB MN ||BC Prove: N is the midpoint of AC M N B C

  10. Proof of Theorem 5.10: D Given: M is the midpoint of AB MN ||BC Prove: N is the midpoint of AC A Paragraph Proof: Let AD be the line through A parallel to MN. M N Then AD, MN , and BC are three parallel lines that cut off congruent segments on transversal AB. By Theorem 5.9 they also cut off congruent segments on AC. Thus AN  NC and N is the midpoint of AC. B C

  11. Theorem 5.11: • The segment that joins the midpoints of two sides of a triangle: • (1) is parallel to the third side • (2) is half as long as the third side A Given: M is the midpoint of AB N is the midpoint of AC Prove: (1) MN || BC (2) MN = ½BC M N B C

  12. Application of Theorem 5.11 B • Given: R, S, and T are midpoints of the sides of ABC. R S A T C

  13. Mixing it all Together Applications of Theorems 5.9, 5.10, and 5.11

  14. Algebraic Connections: Systems Practice If AB = 15, BC = 2x – y, and CD = x + y. Calculate x and y. A E B F C G D H

  15. Algebraic Connections: Perimeter F • P, Q, and R are midpoints of the sides of DEF. • What kind of figure is DPQR? • What is the perimeter of DPQR? 12 Q R 10 E P D 8

  16. Cool Down: Thursday, March 27th Self Test: p. 182 #’s 1 – 8 Remember: Quiz on Sections 5.1 – 5.3 Friday!!

More Related