Unit 9 Presentation SmartBoard.notebook
1
April 24, 2017
Rhombi, Rectanglesand Squares
Return to the Table of ContentsMath Practice
The Response Q's in this lesson address MP1, MP2 & MP7.
Additional Q's to address MP standards:What information are you given? (MP1)What do you need to find? (MP1)How can you represent the problem with numbers and symbols? (MP2)How are the properties of rhombi, rectangles & squares related to algebraic equations? (MP7)
Unit 9 Presentation SmartBoard.notebook
2
April 24, 2017
Three Special Parallelograms
Rhombus Rectangle
Square
All the same properties of a parallelogram apply to the rhombus, rectangle, and square.
Unit 9 Presentation SmartBoard.notebook
3
April 24, 2017
A rhombus is a quadrilateral with four congruent sides.
A B
CD
If AB ≅ BC ≅ CD ≅ DA,then ABCD is a rhombus.
Rhombus
Unit 9 Presentation SmartBoard.notebook
4
April 24, 2017
66 What is the value of y that will make the quadrilateral a rhombus?
A 7.25
B 12
C 20
D 25
35y
12
Answer
C
Unit 9 Presentation SmartBoard.notebook
5
April 24, 2017
67 What is the value of y that will make this parallelogram a rhombus?A 7.25
B 12
C 20
D 25 2y+29
6y
Answer
A
Unit 9 Presentation SmartBoard.notebook
6
April 24, 2017
A B
CD
O
The diagonals of a rhombus are perpendicular.
Since ABCD is a parallelogram, its diagonals bisect each other.
AO ≅ CO and BO ≅ DO.
Theorem
Unit 9 Presentation SmartBoard.notebook
7
April 24, 2017
If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles.
If ABCD is a rhombus, then
∠DAC ≅ ∠BAC ≅∠BCA ≅ ∠DCA
and
∠ADB ≅ ∠CDB ≅ ∠ABD ≅ ∠CBD
Theorem
A B
CD
Unit 9 Presentation SmartBoard.notebook
8
April 24, 2017
68 EFGH is a rhombus. Find the value of x.
E F
G H
72°z°
2x 6
5y
10
Answer
Unit 9 Presentation SmartBoard.notebook
9
April 24, 2017
E F
G H
72°z°
2x 6
5y
10
69 EFGH is a rhombus. Find the value of y.
Answer
Unit 9 Presentation SmartBoard.notebook
10
April 24, 2017
E F
G H
72°z°
2x 6
5y
10
70 EFGH is a rhombus. Find the value of z.
F
Answer
Unit 9 Presentation SmartBoard.notebook
11
April 24, 2017
71 This quadrilateral is a rhombus. Find the value of x.
8
86°
3x + 2
z°
12y2
Answer
Unit 9 Presentation SmartBoard.notebook
12
April 24, 2017
72 This quadrilateral is a rhombus. Find the value of y.
8
86°
3x + 2
z°
12y2
Answer
Unit 9 Presentation SmartBoard.notebook
13
April 24, 2017
73 This quadrilateral is a rhombus. Find the value of z.
8
86°
3x + 2
z°
12y2
Answer
Unit 9 Presentation SmartBoard.notebook
14
April 24, 2017
74 This is a rhombus. Find the value of x.
x°
Answer
90
Unit 9 Presentation SmartBoard.notebook
15
April 24, 2017
75 This is a rhombus. Find the value of x.
13x 3
9
Answer
36
Unit 9 Presentation SmartBoard.notebook
16
April 24, 2017
76 This is a rhombus. Find the value of x.
126°x°
Answer
Unit 9 Presentation SmartBoard.notebook
17
April 24, 2017
77 HJKL is a rhombus. Find the length of HJ.
H J
KL
6 M16
Answer
Unit 9 Presentation SmartBoard.notebook
18
April 24, 2017
A B
CD
A rectangle is a quadrilateral with only right angles.
If ABCD is a rectangle, then ∠A, ∠B, ∠C and ∠ D are right
angles.
If ∠A, ∠B, ∠C and ∠D are right angles, then
ABCD is a rectangle.
Rectangles
Unit 9 Presentation SmartBoard.notebook
19
April 24, 2017
78 What value of y will make the quadrilateral a rectangle?
(6y)°
12 Answer
15
Unit 9 Presentation SmartBoard.notebook
20
April 24, 2017
The diagonals of a rectangle are congruent.
If ABCD is a rectangle, then AC ≅ BD.
Also, since a rectangle is a parallelogram,
AM ≅ BM ≅ CM ≅ DM
A B
CD
M
Theorem
Unit 9 Presentation SmartBoard.notebook
21
April 24, 2017
79 RECT is a rectangle. Find the value of x.
2x 5 13
63°(9y)°
R E
CT
Answer Option A
2x 5 = 132x = 18x = 9
Unit 9 Presentation SmartBoard.notebook
22
April 24, 2017
80 RECT is a rectangle. Find the value of y.
2x 5 13
63°(9y)°
R E
CT
Answer
The measure of each angle in a rectangle is 90°.
Unit 9 Presentation SmartBoard.notebook
23
April 24, 2017
81 RSTU is a rectangle. Find the value of z.
R S
TU(8z)°
Answer
11.25
Unit 9 Presentation SmartBoard.notebook
24
April 24, 2017
82 RSTU is a rectangle. Find the value of z.
R S
TU
4z 9
7
Answer
Unit 9 Presentation SmartBoard.notebook
25
April 24, 2017
A square is a quadrilateral with equal sides and equal angles. It is, therefore both a rhombus and a
rectangle.
A square has all the properties of a rectangle
and rhombus.
Square
Unit 9 Presentation SmartBoard.notebook
26
April 24, 2017
83 This quadrilateral is a square. Find the value of x.
z 4
(5x)°
6
(3y)° Answer
In a rhombus the diagonals are perpendicular.
Unit 9 Presentation SmartBoard.notebook
27
April 24, 2017
84 This quadrilateral is a square. Find the value of y.
z 4
(5x)°
6
(3y)° Answer
In a rhombus the diagonals are perpendicular.
Unit 9 Presentation SmartBoard.notebook
28
April 24, 2017
z 4
(5x)°
6
(3y)°
85 This quadrilateral is a square. Find the value of z.
Answer
Unit 9 Presentation SmartBoard.notebook
29
April 24, 2017
86 This quadrilateral is a square. Find the value of x.
y 2
(12z)°
10 3y
(x2 + 9)°
Answer
Unit 9 Presentation SmartBoard.notebook
30
April 24, 2017
87 This quadrilateral is a square. Find the value of y.
y 2
(12z)°
10 3y
(x2 + 9)° Answer
Unit 9 Presentation SmartBoard.notebook
31
April 24, 2017
88 This quadrilateral is a square. Find the value of z.
y 2
(12z)°
10 3y
(x2 + 9)°
Answer
Unit 9 Presentation SmartBoard.notebook
32
April 24, 2017
89 This quadrilateral is a square. Find the value of y.
(18y)°
Answer
Unit 9 Presentation SmartBoard.notebook
33
April 24, 2017
90 This quadrilateral is a rhombus. Find the value of x.
2x + 6
4x
Answer
Unit 9 Presentation SmartBoard.notebook
34
April 24, 2017
112°
(4x)°
91 The quadrilateral is parallelogram. Find the value of x.
Answer
Unit 9 Presentation SmartBoard.notebook
35
April 24, 2017
92 The quadrilateral is a rectangle. Find the value of x.
10x
3x + 7
Answer
1
Unit 9 Presentation SmartBoard.notebook
36
April 24, 2017
Opposite sidesare ||
Diagonals bisectopposite ∠'s
Has 4 ≅ sides
Has 4 right ∠'sDiagonals are
Fill in the Table with the Correct Definition
rhombus rectangle square
Answer
Opposite sidesare ||
Diagonals are ≅
Unit 9 Presentation SmartBoard.notebook
37
April 24, 2017
Lab Quadrilaterals in the Coordinate Plane
Math Practice
Unit 9 Presentation SmartBoard.notebook
38
April 24, 2017
Trapezoids
Return to theTable of Contents
Unit 9 Presentation SmartBoard.notebook
39
April 24, 2017
A trapezoid is a quadrilateral with one pair of parallel sides.
base
legbase angles
base
leg
The parallel sides are called bases.
The nonparallel sides are called legs.
A trapezoid also has two pairs of base angles.
Trapezoid
Unit 9 Presentation SmartBoard.notebook
40
April 24, 2017
An isosceles trapezoid is a trapezoid with congruent legs.
Isosceles Trapezoid