# In this chapter you will learn about the special properties of quadrilaterals as well as find their perimeters and areas. You will explore the relationships.

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In this chapter you will learn about the special properties of quadrilaterals as well as find their perimeters and areas. You will explore the relationships of the sides and diagonals of a parallelogram, kite, trapezoid, rectangle, and rhombus. Chapter 6 – Quadrilaterals

6.1 What If Both Sides Are Parallel? Pg. 4 Parallelograms

6.1 – What If Both Sides are Parallel?_____ Parallelograms In the past, you used your knowledge to find the area of squares and rectangles. But what if the shape didn't have right angles?

6.1 –PARALLELOGRAMS Find the areas of the figures below. Can you find more than one method for finding the area?

2 4 2 8 un 2

4 12 4 20 un 2

6.2 –AREA OF A PARALLELOGRAM A parallelogram: a four-sided shape with two pairs of parallel sides. How can you find the area of a parallelogram? Consider this question as you answer the questions below.

a. Keesha thinks that the rectangle and parallelograms below have the same area. Her teammate Saundra disagrees. Who is correct? Justify your conclusion.

15 un 2

Area of Parallelogram

b. Does the angle at which the parallelogram slants matter? Why or why not? Explain how you know. No, the base is the same and the height is always perpendicular

A = bh Parallelogram

6.3 – AREA OF PARALLELOGRAMS, CONT. Several more parallelograms are shown below. In each case, find a related rectangle for which you know both the base and height. Rotating your packet might help. Use what you know about rectangles to find the area of each parallelogram.

A = bh A = (9)(4) A = 36un 2

A = bh A = (20)(5) A = 100un 2

A = bh A = (7)(3) A = 21un 2

Definition: If a quadrilateral is a parallelogram, then both pairs of ________________ sides are ______________. opposite parallel

If a quadrilateral is a parallelogram, then both pairs of ________________ sides are ______________. opposite congruent

If a quadrilateral is a parallelogram, then both pairs of ________________ angles are ________________. opposite congruent

If a quadrilateral is a parallelogram, then both pairs of _______________ angles are ___________________. consecutive supplementary x y xy

If a quadrilateral is a parallelogram, then the diagonals _______________ each other. bisect

6.5 –PARALLELOGRAM PARTS Find the value of each variable in the parallelogram.

a – 3 = 14 a = 17 b + 2 = 7 b = 5

3x + 6 = 12 2y + 9 = 27 2y = 18 3x = 6 x = 2 y = 9

130° 50°

9b – 2 = 106 9b = 108 b = 12 7a – 3 + 106 = 180 7a + 103 = 180 a = 11 7a = 77

If opposite sides of a quadrilateral are ________________, then the quadrilateral is a ________________. congruent parallelogram

If both pairs of opposite angles are _________________, then the quadrilateral is a _________________. congruent parallelogram

If consecutive angles are ________________, then the quadrilateral is a ________________. supplementary parallelogram

If the diagonals ____________ each other, then the quadrilateral is a ________________. bisect parallelogram

If one pair of opposite sides are ____________ and ____________, then the quadrilateral is a ________________. congruent parallelogram parallel New!!!

6.6 –PROVING PARALLELOGRAMS Can you prove the quadrilaterals are parallelograms? Why or why not?

yes One pair of opposite sides parallel and congruent yes Both pairs of opposite angles are congruent

no Parallel and congruent marks are not on the same sides. yes Both pairs of opposite sides are congruent

yes Both pairs of opposite sides are parallel no Only one pair of congruent angles

yes Diagonals bisect each other

6.7 –PARALLELOGRAM IDENTIFICATION The definition of a parallelogram is, "A quadrilateral with both opposite sides parallel." Based on this definition, circle all parallelograms below.

A B C D a. What is the slopes of all four line segments? AB = ______ BC = ______ CD = ______ AD = ______ 2 7 2727 8 1 8181 2727 8181

A B C D b. What is the relationship between these sides, given the slopes? Explain. AB = ______ BC = ______ CD = ______ AD = ______ 2 7 2727 A 8 1 8181 2727 8181 Both opposite sides are parallel

A B C D c. What is the length of all four line segments? AB = ______ BC = ______ CD = ______ AD = ______ 2 7 A 8 1 2 2 + 7 2 = d 2 4 + 49 = d 2 53 = d 2 1 2 + 8 2 = d 2 1 + 64 = d 2 65 = d 2

A B C D d. What is the relationship between these sides, given their length? Explain. AB = ______ BC = ______ CD = ______ AD = ______ 2 7 A 8 1 Both opposite sides are congruent

A B C D e. What kind of quadrilateral is this? How do you know? 2 7 A 8 1 Parallelogram, Both opposite sides are parallel and congruent

Parallelogram Rectangle Rhombus Square Trapezoid Isosceles Trapezoid Kite Triangle

Name Block #

Parallelogram

Both opposite sides parallel Both opposite sides congruent Both opposite angles congruent Consecutive angles supplementary Diagonals bisect each other

Triangle

3 sides

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