Download presentation

1
**6-2 Properties of Parallelograms page 294**

Objective: To use relationships among sides, angles, diagonals or transversals of parallelograms.

2
**Vocabulary Consecutive angles – angles of a polygon that share a side.**

NOTE: Consecutive angles of a parallelogram are supplementary. A B C D

3
You can use what you know about parallel lines & transversals to prove some theorems about parallelograms Theorem 6.1 p Opposite sides of a parallelogram are congruent

4
**Theorem 6-1 Opposite sides of a parallelogram are congruent. AB = DC**

AD = BC A B D C

5
**Properties of Parallelograms**

Use KMOQ to find m O. Q and O are consecutive angles of KMOQ, so they are supplementary. Definition of supplementary angles m O + m Q = 180 Substitute 35 for m Q. m O + 35 = 180 Subtract 35 from each side. m O = 145 6-2

6
**Theorem 6-2 Opposite angle of a parallelogram are congruent.**

<A = <C <B = <D A B D C

7
**Find the value of x in ABCD. Then find m A.**

x + 15 = 135 – x Opposite angles of a are congruent. 2x + 15 = 135 Add x to each side. 2x = 120 Subtract 15 from each side. x = 60 Divide each side by 2. Substitute 60 for x. m B = = 75 Consecutive angles of a parallelogram are supplementary. m A + m B = 180 m A + 75 = 180 Substitute 75 for m B. Subtract 75 from each side. m A = 105 6-2

8
Theorem 6-3 The diagonals of a parallelogram bisect each other.

9
**Properties of Parallelograms**

Find the values of x and y in KLMN. x = 7y – 16 The diagonals of a parallelogram bisect each other. 2x + 5 = 5y 2(7y – 16) + 5 = 5y Substitute 7y – 16 for x in the second equation to solve for y. 14y – = 5y Distribute. 14y – 27 = 5y Simplify. –27 = –9y Subtract 14y from each side. 3 = y Divide each side by –9. x = 7(3) – 16 Substitute 3 for y in the first equation to solve for x. x = 5 Simplify. So x = 5 and y = 3. 6-2

10
Theorem 6-4 If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal. BD = DF A B C D E F

11
Closure Lesson 6-1 defined a rectangle as a parallelogram with four right angles. Explain why you can now define a rectangle as a parallelogram with one right angle.

12
**Summary What is true about the opposite sides of a parallelogram?**

What is true about the opposite angles of a parallelogram? What about consecutive angles? What about the diagonals of a parallelogram? When 3 or more parallel lines cut of congruent segments on one transversal, what is true about all other transversals?

13
Assignment 6.2 Page 297 #2-32 E, 34, 35, 39-41

Similar presentations

Presentation is loading. Please wait....

OK

6.2 Parallelograms.

6.2 Parallelograms.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To ensure the functioning of the site, we use **cookies**. We share information about your activities on the site with our partners and Google partners: social networks and companies engaged in advertising and web analytics. For more information, see the Privacy Policy and Google Privacy & Terms.
Your consent to our cookies if you continue to use this website.

Ads by Google

Ppt on vegetarian and non vegetarian photo Interactive ppt on the writing process Free ppt on etiquettes of life Ppt on paintings and photographs related to colonial period definition Numeric display ppt online Ppt on paintings and photographs related to colonial period years Ppt on drugs abused Ppt on power diode for microwave Ppt on magnetohydrodynamic power generation Ppt on contact dermatitis