Download presentation
Presentation is loading. Please wait.
Published byDerick Hubbard Modified over 9 years ago
1
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
6.1 What If Both Sides Are Parallel? Pg. 4 Parallelograms
7
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?
8
6.1 –PARALLELOGRAMS Find the areas of the figures below. Can you find more than one method for finding the area?
9
2 4 2 8 un 2
10
4 12 4 20 un 2
11
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.
12
a. Keesha thinks that the rectangle and parallelograms below have the same area. Her teammate Saundra disagrees. Who is correct? Justify your conclusion.
13
15 un 2
15
Area of Parallelogram
16
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
17
A = bh Parallelogram
18
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.
19
A = bh A = (9)(4) A = 36un 2
20
A = bh A = (20)(5) A = 100un 2
21
A = bh A = (7)(3) A = 21un 2
22
Definition: If a quadrilateral is a parallelogram, then both pairs of ________________ sides are ______________. opposite parallel
23
If a quadrilateral is a parallelogram, then both pairs of ________________ sides are ______________. opposite congruent
24
If a quadrilateral is a parallelogram, then both pairs of ________________ angles are ________________. opposite congruent
25
If a quadrilateral is a parallelogram, then both pairs of _______________ angles are ___________________. consecutive supplementary x y xy
26
If a quadrilateral is a parallelogram, then the diagonals _______________ each other. bisect
27
6.5 –PARALLELOGRAM PARTS Find the value of each variable in the parallelogram.
28
a – 3 = 14 a = 17 b + 2 = 7 b = 5
29
3x + 6 = 12 2y + 9 = 27 2y = 18 3x = 6 x = 2 y = 9
30
130° 50°
31
9b – 2 = 106 9b = 108 b = 12 7a – 3 + 106 = 180 7a + 103 = 180 a = 11 7a = 77
32
If opposite sides of a quadrilateral are ________________, then the quadrilateral is a ________________. congruent parallelogram
33
If both pairs of opposite angles are _________________, then the quadrilateral is a _________________. congruent parallelogram
34
If consecutive angles are ________________, then the quadrilateral is a ________________. supplementary parallelogram
35
If the diagonals ____________ each other, then the quadrilateral is a ________________. bisect parallelogram
36
If one pair of opposite sides are ____________ and ____________, then the quadrilateral is a ________________. congruent parallelogram parallel New!!!
37
6.6 –PROVING PARALLELOGRAMS Can you prove the quadrilaterals are parallelograms? Why or why not?
38
yes One pair of opposite sides parallel and congruent yes Both pairs of opposite angles are congruent
39
no Parallel and congruent marks are not on the same sides. yes Both pairs of opposite sides are congruent
40
yes Both pairs of opposite sides are parallel no Only one pair of congruent angles
41
yes Diagonals bisect each other
42
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.
Similar presentations
© 2024 SlidePlayer.com. Inc.
All rights reserved.