1 / 44

Quadrilaterals

Quadrilaterals. § 8.1 Quadrilaterals. § 8.2 Parallelograms. § 8.3 Tests for Parallelograms. § 8.4 Rectangles, Rhombi, and Squares. § 8.5 Trapezoids. Vocabulary. Quadrilaterals. What You'll Learn.

nico
Download Presentation

Quadrilaterals

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. Quadrilaterals • § 8.1 Quadrilaterals • § 8.2 Parallelograms • § 8.3 Tests for Parallelograms • § 8.4 Rectangles, Rhombi, and Squares • § 8.5 Trapezoids

  2. Vocabulary Quadrilaterals What You'll Learn You will learn to identify parts of quadrilaterals and find thesum of the measures of the interior angles of a quadrilateral. 1) Quadrilateral 2) Consecutive 3) Nonconsecutive 4) Diagonal

  3. Quadrilaterals four four A quadrilateral is a closed geometric figure with ____ sides and ____ vertices. The segments of a quadrilateral intersect only at their endpoints. Special types of quadrilaterals include squares and rectangles.

  4. Quadrilaterals Quadrilaterals are named by listing their vertices in order. There are several names for the quadrilateral below. Some examples: quadrilateral ABCD B quadrilateral BCDA A quadrilateral CDAB or quadrilateral DABC D C

  5. Q P S R Quadrilaterals consecutive Any two _______ of a quadrilateral are either __________ or _____________. vertices sides angles nonconsecutive

  6. Q P S R Quadrilaterals Segments that join nonconsecutive vertices of a quadrilateral are called________. diagonals R and P arenonconsecutivevertices. S and Q arenonconsecutivevertices.

  7. Q T R S Quadrilaterals Name all pairs of consecutive sides: Name all pairs of nonconsecutive angles: Name the diagonals:

  8. A B D C 360 Quadrilaterals Considering the quadrilateral to the right. 1 What shapes are formed if a diagonal is drawn? ___________ two triangles 2 3 5 4 Use the Angle Sum Theorem (Section 5-2)to find m1 + m2 + m3 180 Use the Angle Sum Theorem (Section 5-2)to find m4 + m5 + m6 180 6 180 Find m1 + m2 + m3 + m4 + m5 + m6 + 180 This leads to the following theorem.

  9. b° a° c° d° Quadrilaterals 360 360 a + b + c + d =

  10. B A C D Quadrilaterals Find the measure of B in quadrilateral ABCD if A = x, B = 2x,C = x – 10, and D = 50. mA + mB + mC + mD = 360 x + 2x + x – 10 + 50 = 360 4x + 40 = 360 4x = 320 x = 80 B = 2x B = 2(80) B = 160

  11. Quadrilaterals End of Section 8.1

  12. Vocabulary Parallelograms What You'll Learn You will learn to identify and use the properties of parallelograms. 1) Parallelogram

  13. In parallelogram ABCD below, and B A D C Parallelograms parallel sides A parallelogram is a quadrilateral with two pairs of ____________. congruent Also, the parallel sides are _________. Knowledge gained about “parallels” (chapter 4)will now be used in the following theorems.

  14. A A A B B B D D D C C C Parallelograms Opposite angles of a parallelogram are ________. congruent A  C and B  D Opposite sides of a parallelogram are ________. congruent The consecutive angles of a parallelogram are ____________. supplementary mA + mB = 180mD + mC = 180

  15. In RSTU, RS = 45, ST = 70, and U = 68. S R 45 70 U T 68° Parallelograms Find: RU = ____ 70 Theorem 8-3 45 UT = _____ Theorem 8-3 68° Theorem 8-2 mS = _____ 112° Theorem 8-4 mT = _____

  16. In RSTU, if RT = 56, find RE. A B R D S C E U T Parallelograms bisect E RE = 28

  17. A B D C Parallelograms In the figure below, ABCD is a parallelogram. Since AD || BC and diagonal DB is a transversal, then ADB  CBD. (Alternate Interior angles) Since AB || DC and diagonal DB is a transversal, then BDC  DBA. (Alternate Interior angles) DB  BD ASA Theorem

  18. A B D C Parallelograms congruent triangles

  19. Parallelograms The Escher design below is based ona _____________. parallelogram You can use a parallelogram to make a simple Escher-like drawing. Change one side of the parallelogram and then translate (slide) the change to the opposite side. The resulting figure is used to make a design with different colors and textures.

  20. Parallelograms End of Section 8.2

  21. Vocabulary Tests for Parallelograms What You'll Learn You will learn to identify and use tests to show that a quadrilateral is a parallelogram. Nothing New!

  22. A B C D Tests for Parallelograms congruent

  23. In quadrilateral PQRS, PR and QS bisect each other at T. P Q T S R Tests for Parallelograms You can use the properties of congruent triangles and Theorem 8-7 to find other ways to show that a quadrilateral is a parallelogram. Show that PQRS is a parallelogram by providing a reason for each step. Definition of segment bisector Vertical angles are congruent SAS Corresp. parts of Congruent Triangles are Congruent Theorem 8-7

  24. A B C D Tests for Parallelograms parallel congruent

  25. A B E D C Tests for Parallelograms bisect each other

  26. A B D C Tests for Parallelograms Determine whether each quadrilateral is a parallelogram.If the figure is a parallelogram, give a reason for your answer. Given Alt. Int. Angles Therefore, quadrilateral ABCD is a parallelogram. Theorem 8-8

  27. Tests for Parallelograms End of Section 8.3

  28. Vocabulary Rectangles, Rhombi, and Squares What You'll Learn You will learn to identify and use the properties of rectangles, rhombi, and squares. 1) Rectangle 2) Rhombus 3) Square

  29. Rectangles, Rhombi, and Squares A closed figure, 4 sides & 4 vertices Quadrilateral Opposite sides parallel opposite sides congruent Parallelogram Parallelogram with 4 congruent sides Parallelogram with 4 right angles Rhombus Rectangle Parallelogram with 4 congruent sides and 4 right angles Square

  30. B A D C Rectangles, Rhombi, and Squares Identify the parallelogram below. Identify the parallelogram below. rhombus Parallelogram ABCD has 4 right angles, but the four sides are not congruent. Therefore, it is a _________ rectangle

  31. A B C D Rectangles, Rhombi, and Squares congruent

  32. B A C D Rectangles, Rhombi, and Squares perpendicular

  33. Rectangles, Rhombi, and Squares bisects A 1 2 D 8 7 6 5 C 3 4 B

  34. Y X O W Z 3) Name all segments that are congruent to WO. Explain your reasoning. OY, XO, and OZ Rectangles, Rhombi, and Squares Use square XYZW to answer the following questions: 14 1) If YW = 14, XZ = ____ A square has all the properties of a rectangle, and the diagonals of a rectangle are congruent. 90 2) mYOX = ____ A square has all the properties of a rhombus, and the diagonals of a rhombus are perpendicular. The diagonals are congruent and they bisect each other.

  35. Quadrilaterals Parallelograms Rectangles Rhombi Squares Rectangles, Rhombi, and Squares Use the Venn diagram to answer the following questions: T or F T 1) Every square is a rhombus: ___ 5) All rhombi are parallelograms: ___ T F 2) Every rhombus is a square: ___ F 3) Every rectangle is a square: ___ 6) Every parallelogram is a rectangle: ___ F T 4) Every square is a rectangle: ___

  36. Rectangles, Rhombi, and Squares End of Section 8.4

  37. Vocabulary Trapezoids What You'll Learn You will learn to identify and use the properties of trapezoidsand isosceles trapezoids. 1) Trapezoid

  38. R T A P Trapezoids parallel sides quadrilateral A trapezoid is a ____________ with exactly one pair of ____________. The parallel sides are called ______. bases legs The non parallel sides are called _____. base Each trapezoid has two pair of base angles. leg leg base angles T and R are one pair of base angles. P and A are the other pair of base angles. base

  39. A B N M D C Trapezoids bases and the length of the median equals _______________ of the lengths of the bases. one-half the sum

  40. A B M N D C Trapezoids Find the length of median MN in trapezoid ABCD if AB = 16 and DC = 20 16 18 20

  41. Trapezoids If the legs of a trapezoid are congruent, the trapezoid is an _________________. isosceles trapezoid In lesson 6 – 4, you learned that the base angles of an isosceles triangle are congruent. There is a similar property of isosceles trapezoids.

  42. W X Z Y Trapezoids base angles

  43. R T 60° P A Trapezoids Find the missing angle measures in isosceles trapezoid TRAP. Theorem 8 – 14 P  A 120° 120° mP = mA 60 = mA Theorem 8 – 14 T  R 60° P + A + 2(T) = 360 60 + 60 + 2(T) = 360 120 + 2(T) = 360 2(T) = 240 T = 120 R = 120

  44. Trapezoids End of Section 8.5

More Related