6.4 rhombuses, rectangles, and squares review find the value of the variables. 52° 68° h p...
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![Page 1: 6.4 Rhombuses, Rectangles, and Squares Review Find the value of the variables. 52° 68° h p (2p-14)° 50° 52° + 68° + h = 180° 120° + h = 180 ° h = 60°](https://reader035.vdocuments.net/reader035/viewer/2022062417/5514dc6b55034640138b6615/html5/thumbnails/1.jpg)
6.4 Rhombuses, Rectangles, and Squares
![Page 2: 6.4 Rhombuses, Rectangles, and Squares Review Find the value of the variables. 52° 68° h p (2p-14)° 50° 52° + 68° + h = 180° 120° + h = 180 ° h = 60°](https://reader035.vdocuments.net/reader035/viewer/2022062417/5514dc6b55034640138b6615/html5/thumbnails/2.jpg)
Review
Find the value of the variables.
52°
68°
h
p
(2p-14)° 50°
52° + 68° + h = 180°
120° + h = 180 °
h = 60°
p + 50° + (2p – 14)° = 180°p + 2p + 50° - 14° = 180° 3p + 36° = 180° 3p = 144 °
p = 48 °
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Special Parallelograms
Rhombus A rhombus is a parallelogram with four
congruent sides.
![Page 4: 6.4 Rhombuses, Rectangles, and Squares Review Find the value of the variables. 52° 68° h p (2p-14)° 50° 52° + 68° + h = 180° 120° + h = 180 ° h = 60°](https://reader035.vdocuments.net/reader035/viewer/2022062417/5514dc6b55034640138b6615/html5/thumbnails/4.jpg)
Special Parallelograms
Rectangle A rectangle is a parallelogram with four right
angles.
![Page 5: 6.4 Rhombuses, Rectangles, and Squares Review Find the value of the variables. 52° 68° h p (2p-14)° 50° 52° + 68° + h = 180° 120° + h = 180 ° h = 60°](https://reader035.vdocuments.net/reader035/viewer/2022062417/5514dc6b55034640138b6615/html5/thumbnails/5.jpg)
Special Parallelogram
Square A square is a parallelogram with four
congruent sides and four right angles.
![Page 6: 6.4 Rhombuses, Rectangles, and Squares Review Find the value of the variables. 52° 68° h p (2p-14)° 50° 52° + 68° + h = 180° 120° + h = 180 ° h = 60°](https://reader035.vdocuments.net/reader035/viewer/2022062417/5514dc6b55034640138b6615/html5/thumbnails/6.jpg)
Corollaries
Rhombus corollary A quadrilateral is a rhombus if and only if it
has four congruent sides.
Rectangle corollary A quadrilateral is a rectangle if and only if it
has four right angles.
Square corollary A quadrilateral is a square if and only if it is a
rhombus and a rectangle.
![Page 7: 6.4 Rhombuses, Rectangles, and Squares Review Find the value of the variables. 52° 68° h p (2p-14)° 50° 52° + 68° + h = 180° 120° + h = 180 ° h = 60°](https://reader035.vdocuments.net/reader035/viewer/2022062417/5514dc6b55034640138b6615/html5/thumbnails/7.jpg)
Example
PQRS is a rhombus. What is the value of b?
P Q
RS
2b + 3
5b – 6
2b + 3 = 5b – 6 9 = 3b 3 = b
![Page 8: 6.4 Rhombuses, Rectangles, and Squares Review Find the value of the variables. 52° 68° h p (2p-14)° 50° 52° + 68° + h = 180° 120° + h = 180 ° h = 60°](https://reader035.vdocuments.net/reader035/viewer/2022062417/5514dc6b55034640138b6615/html5/thumbnails/8.jpg)
Review
In rectangle ABCD, if AB = 7f – 3 and CD = 4f + 9, then f = ___
A) 1
B) 2
C) 3
D) 4
E) 5
7f – 3 = 4f + 9
3f – 3 = 9
3f = 12
f = 4
![Page 9: 6.4 Rhombuses, Rectangles, and Squares Review Find the value of the variables. 52° 68° h p (2p-14)° 50° 52° + 68° + h = 180° 120° + h = 180 ° h = 60°](https://reader035.vdocuments.net/reader035/viewer/2022062417/5514dc6b55034640138b6615/html5/thumbnails/9.jpg)
Example
PQRS is a rhombus. What is the value of b?
P Q
RS
3b + 12
5b – 6
3b + 12 = 5b – 6 18 = 2b 9 = b
![Page 10: 6.4 Rhombuses, Rectangles, and Squares Review Find the value of the variables. 52° 68° h p (2p-14)° 50° 52° + 68° + h = 180° 120° + h = 180 ° h = 60°](https://reader035.vdocuments.net/reader035/viewer/2022062417/5514dc6b55034640138b6615/html5/thumbnails/10.jpg)
Theorems for rhombus
A parallelogram is a rhombus if and only if its diagonals are perpendicular.
A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.
L
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Theorem of rectangle
A parallelogram is a rectangle if and only if its diagonals are congruent.
A B
CD
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Match the properties of a quadrilateral
1. The diagonals are congruent
2. Both pairs of opposite sides are congruent
3. Both pairs of opposite sides are parallel
4. All angles are congruent
5. All sides are congruent
6. Diagonals bisect the angles
A. Parallelogram
B. Rectangle
C. Rhombus
D. Square
B,D
A,B,C,D
A,B,C,D
B,D
C,D
C
![Page 13: 6.4 Rhombuses, Rectangles, and Squares Review Find the value of the variables. 52° 68° h p (2p-14)° 50° 52° + 68° + h = 180° 120° + h = 180 ° h = 60°](https://reader035.vdocuments.net/reader035/viewer/2022062417/5514dc6b55034640138b6615/html5/thumbnails/13.jpg)
Decide if the statement is sometimes, always, or never true.1. A rhombus is equilateral.
2. The diagonals of a rectangle are _|_.
3. The opposite angles of a rhombus are supplementary.
4. A square is a rectangle.
5. The diagonals of a rectangle bisect each other.
6. The consecutive angles of a square are supplementary.
Always
Quadrilateral ABCD is Rhombus.7. If m <BAE = 32o, find m<ECD.8. If m<EDC = 43o, find m<CBA.9. If m<EAB = 57o, find m<ADC.10. If m<BEC = (3x -15)o, solve for x.11. If m<ADE = ((5x – 8)o and m<CBE = (3x +24)o, solve for x12. If m<BAD = (4x + 14)o and m<ABC = (2x + 10)o, solve for x.
A B
E
D C
32o
Sometimes
Sometimes
Always
Always
Always
86o
66o
35o
16 26
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Coordinate Proofs Using the Properties of Rhombuses, Rectangles and Squares
Using the distance formula and slope, how can we determine the specific shape of a parallelogram?
Rhombus –
Rectangle –
Square -
Based on the following Coordinate values, determine if each parallelogramis a rhombus, a rectangle, or square.
P (-2, 3) P(-4, 0)Q(-2, -4) Q(3, 7)R(2, -4) R(6, 4)S(2, 3) S(-1, -3)
1. Show all sides are equal distance
2. Show all diagonals are perpendicular.
1. Show diagonals are equal distance
2. Show opposite sides are perpendicular
Show one of the above four ways.
RECTANGLE RECTANGLE