Bell Ringer

Rhombus, Rectangles, and Squares

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

In the diagram, ABCD is a rectangle. Example 1 Use Properties of Special Parallelograms In the diagram, ABCD is a rectangle. Find AD and AB. a. b. Find mA, mB, mC, and mD. 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. By definition, a rectangle has four right angles, so mA = mB = mC = mD = 90°. b. 4

Now You Try  In the diagram, PQRS is a rhombus. Find QR, RS, and SP. 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 5

Use the information in the diagram to name the special quadrilateral. Example 2 Identify Special Quadrilaterals 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. 6

Now You Try  Identify Special Quadrilaterals Use the information in the diagram to name the special quadrilateral. 2. ANSWER rhombus 3. ANSWER square 7

ABCD is a rhombus. Find the value of x. Example 3 Use Diagonals of a Rhombus ABCD is a rhombus. Find the value of x. SOLUTION By Theorem 6.10, the diagonals of a rhombus are perpendicular. Therefore, BEC is a right angle, so ∆BEC is a right triangle. By the Corollary to the Triangle Sum Theorem, the acute angles of a right triangle are complementary. So, x = 90 – 60 = 30. 8

The diagonals measure 7 ft 4 in. and Example 4 Use Diagonals of a Rectangle You nail four pieces of wood together to build a four-sided frame, as shown. What is the shape of the frame? a. The diagonals measure 7 ft 4 in. and 7 ft 2 in. Is the frame a rectangle? b. SOLUTION The frame is a parallelogram because both pairs of opposite sides are congruent. a. b. The frame is not a rectangle because the diagonals are not congruent. 9

Now You Try  Find the value of x. rhombus ABCD 4. ANSWER 90 Use Diagonals Find the value of x. rhombus ABCD 4. ANSWER 90 rectangle EFGH 5. ANSWER 12 square JKLM 6. ANSWER 45 10

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Now You Try  19. A B ABCD is a square find x 5x D C

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Complete Pages 328-330 #s 8-30 Even only