1 / 23

6.1 Classifying Quadrilaterals page 288

6.1 Classifying Quadrilaterals page 288. Obj 1: To define & classify special types of quadrilaterals. And why…. To use the properties of special quadrilaterals with a kite, as in Example 3. Seven important types of quadrilaterals …. Parallelogram -has both pairs of opposite sides parallel

isla
Download Presentation

6.1 Classifying Quadrilaterals page 288

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. 6.1 Classifying Quadrilateralspage 288 Obj 1: To define & classify special types of quadrilaterals

  2. And why… • To use the properties of special quadrilaterals with a kite, as in Example 3.

  3. Seven important types of quadrilaterals … • Parallelogram-has both pairs of opposite sides parallel • Rhombus-has four congruent sides • Rectangle-has four right angles • Square-has four congruent sides and four right angles • Kite-has two pairs of adjacent sides congruent and no opposite opposite sides congruent.

  4. Continued…. • Trapezoid-has exactly one pair of parallel sides. (you have same side interior angles) • Isosceles trapezoid-is a trapezoid whose non-parallel opposite sides are congruent

  5. It is a trapezoid because AB and DC appear parallel and AD and BC appear nonparallel. Classifying Quadrilaterals Judging by appearance, classify ABCD in as many ways as possible. ABCD is a quadrilateral because it has four sides. 6-1

  6. You try one • Turn to page 289 and complete check understanding 1 (top of page)

  7. Classifying by Coordinate Method • Do you remember the slope formula? • Do you remember the distance formula that finds the distance between two points?

  8. Do you remember how to tell if two lines are parallel? • Do you remember how to tell if two lines are perpendicular?

  9. Graph quadrilateral QBHA. First, find the slope of each side. slope of QB = slope of BH = slope of HA = slope of QA = 4 – 4 –4 – 10 9 – 9 8 – (–2) 4 – 9 10 – 8 9 – 4 –2 – (–4) 5 2 5 2 = = = = – 0 0 BH is parallel to QA because their slopes are equal. QB is not parallel to HA because their slopes are not equal. Classifying Quadrilaterals Determine the most precise name for the quadrilateral with vertices Q(–4, 4), B(–2, 9), H(8, 9), and A(10, 4). 6-1

  10. Next, use the distance formula to see whether any pairs of sides are congruent. QB = ( –2 – ( –4))2 + (9 – 4)2 = 4 + 25 = 29 HA = (10 – 8)2 + (4 – 9)2 = 4 + 25 = 29 BH = (8 – (–2))2 + (9 – 9)2 = 100 + 0 =10 QA = (– 4 – 10)2 + (4 – 4)2 = 196 + 0 = 14 Classifying Quadrilaterals (continued) One pair of opposite sides are parallel, so QBHA is a trapezoid. Because QB = HA, QBHA is an isosceles trapezoid. 6-1

  11. You try one • Turn to page 289 and complete check understanding 2 (bottom of page).

  12. In parallelogram RSTU, mR = 2x – 10 and m S = 3x + 50. Find x. If lines are parallel, then interior angles on the same side of a transversal are supplementary. m R + m S = 180 Draw quadrilateral RSTU. Label R and S. RSTU is a parallelogram. Given ST || RU Definition of parallelogram Classifying Quadrilaterals 6-1

  13. (continued) (2x – 10) + (3x + 50) = 180 Substitute 2x – 10 for m R and 3x + 50 for m S. 5x + 40 = 180 Simplify. 5x = 140 Subtract 40 from each side. x = 28 Divide each side by 5. Classifying Quadrilaterals 6-1

  14. You try one • Turn to page 290 and complete check understanding 3 (middle of page)

  15. Summary 6.1 • What are the seven types of quadrilaterals we have described today? • How do you tell if two lines are parallel? • How do you tell if two lines are perpendicular?

  16. 6.2 Properties of Parallelograms (page 294) • Obj 1: to use relationships among sides & among angles of parallelograms • Obj 2: to use relationships involving diagonals of parallelograms & transversals

  17. You can use what you know about parallel lines & transversals to prove some theorems about parallelograms • Theorem 6.1 p. 294---Opposite sides of a parallelogram are congruent

  18. Theorems Continued… • Theorem 6.2 page 295 –Opposite angles of a parallelogram are congruent • Theorem 6.3 page 296—the diagonals of a parallelogram bisect each other • Theorem 6.4 page 297—If three of more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transveral.

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

  20. 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 = 60 + 15 = 75 m A + m B = 180 Consecutive angles of a parallelogram are supplementary. m A + 75 = 180 Substitute 75 for m B. m A = 105 Subtract 75 from each side. Properties of Parallelograms GEOMETRY LESSON 6-2 Find the value of x in ABCD. Then find m A. 6-2

  21. 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 – 32 + 5 = 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

  22. Summary 6.2 What are the properties of parallelograms? Theorem 6.1- Theorem 6.2- Theorem 6.3- Theorem 6.4-

  23. Homework 6.1 page 290 2-26 E, 37-42

More Related