1 / 15

Properties of Parallelograms: Sides, Angles, and Diagonals

Learn the properties of parallelograms, including their sides, angles, and diagonals. Discover the theorems that govern these properties and apply them in solving problems. Homework exercises included.

lbroadnax
Download Presentation

Properties of Parallelograms: Sides, Angles, and Diagonals

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. Geometry Lesson 6 – 2 Parallelograms Objective: Recognize and apply properties of the sides of angles of parallelograms. Recognize and apply properties of the diagonals of parallelograms.

  2. Parallelograms • What is a parallelogram? • A quadrilateral with both pairs of opposite sides parallel. • To name a parallelogram:

  3. Theorems:Properties of Parallelograms • Theorem 6.3 • If a quadrilateral is a parallelogram, then its opposite sides are congruent.

  4. Theorem • Theorem 6.4 • If a quadrilateral is a parallelogram, then its opposite angles are congruent.

  5. Theorem • Theorem 6.5 • If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

  6. Theorem • Theorem 6.6 • If a parallelogram has one right angle, then it has four right angles.

  7. In parallelogram ABCD, suppose the measure of angle A is 55, segment AB is 2.5 feet, and segment BC is 1 foot. Find each measure. • Find DC 2.5 180 – 55 = 125 55

  8. Theorems:Diagonals of Parallelograms • Theorem 6.7 • If a quadrilateral is a parallelogram, then its diagonals bisect each other.

  9. Theorem • Theorem 6.8 • If a quadrilateral is a parallelogram, then each diagonal separates the parallelogram into two congruent triangles.

  10. 5x = 27 If QRST is a parallelogram, find the following. • Find x • Find y • Find z Opps. Sides equal x = 5.4 Diagonals bisect 2y – 5 = y + 4 y = 9 Alt. Interior angles are congruent. 3z = 33 z = 11

  11. Find the value of each variable in the parallelograms. 3z – 4 = z + 5 4x + 2x – 6 = 180 6x – 6 = 180 2z = 9 6x = 186 z = 4.5 x = 31 y + 8 = 5y 2 = y

  12. Determine the coordinates of the intersection of the diagonals of parallelogram FGHJ with vertices F (-2, 4) G (3, 5) H (2, -3) and J (-3, -4) • What do you know about the diagonals of a parallelogram? • Since we know they bisect what is a good point to find? • Find the Midpoint of the diagonals: Double check:

  13. Determine the coordinates of the intersection of the diagonals of RSTU with vertices R (-8, -2) S (-6, 7) T (6, 7) and U (4, -2)

  14. 1. 1. Given 2. Opp. Sides congruent. 2. 3. 3. Transitive

  15. Homework • Pg. 403 1 – 6 all, 10 – 22 E, 44 – 60 E

More Related