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Bell Ringer
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Rhombus, Rectangles, and Squares
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Rhombus- is a parallelogram with four congruent sides.
Rectangle – is a parallelogram with four right angles
Square – is a parallelogram with four congruent sides and four right angles
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Use Properties of Special ParallelogramsExample 1
In the diagram, ABCD is a rectangle.
Find AD and AB.a.
By definition, a rectangle has four right angles, so mA = mB = mC = mD = 90°.
b.
SOLUTION
By definition, a rectangle is a parallelogram, so ABCD is a parallelogram. Because opposite sides of a parallelogram are congruent, AD = BC = 5 and AB = DC = 8.
a.
b. Find mA, mB, mC, and mD.
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Now You Try Use Properties of Special Parallelograms
In the diagram, PQRS is a rhombus.Find QR, RS, and SP.
1.
ANSWER QR = 6, RS = 6, SP = 6
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Identify Special QuadrilateralsExample 2
Use the information in the diagram to name the special quadrilateral.
SOLUTION
Because all of the sides are not the same length, you know that the quadrilateral is not a square.
The quadrilateral has four right angles. So, by the Rectangle Corollary, the quadrilateral is a rectangle.
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Now You Try Identify Special Quadrilaterals
ANSWER rhombus
ANSWER square
Use the information in the diagram to name the special quadrilateral.
2.
3.
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Use Diagonals of a RhombusExample 3
ABCD is a rhombus. Find the value of x.
By the Corollary to the Triangle Sum Theorem, the acute angles of a right triangle are complementary. So, x = 90 – 60 = 30.
SOLUTION
By Theorem 6.10, the diagonals of a rhombus are perpendicular. Therefore, BEC is a right angle, so ∆BEC is a right triangle.
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Use Diagonals of a RectangleExample 4
b. The frame is not a rectangle because the diagonals are not congruent.
SOLUTION
The frame is a parallelogram because both pairs of opposite sides are congruent.
a.
The diagonals measure 7 ft 4 in. and7 ft 2 in. Is the frame a rectangle?
b.
You nail four pieces of wood together to build a four-sided frame, as shown. What is the shape of the frame?
a.
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Now You Try Use Diagonals
ANSWER 90
ANSWER 12
ANSWER 45
Find the value of x.
rhombus ABCD4.
rectangle EFGH5.
square JKLM6.
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Now You Try
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Now You Try
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Now You Try
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Now You Try
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Now You Try
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A B
CD
5xABCD is a square
find x
19.Now You Try
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Page 328
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Complete Pages 328-330#s 8-30 Even only