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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. SOLUTION. a.
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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
SOLUTION a. By definition, a rectangle is a parallelogram, so ABCDis a parallelogram. Because opposite sides of a parallelogram are congruent, AD = BC = 5 andAB = DC = 8. b. By definition, a rectangle has four right angles, so mA = mB = mC = mD = 90°. Example 1 Use Properties of Special Parallelograms In the diagram, ABCDis a rectangle. a. Find ADand AB. b. Find mA, mB, mC, and mD.
Now You Try 1. In the diagram, PQRSis a rhombus. Find QR, RS, and SP. QR = 6,RS = 6, SP = 6 ANSWER Use Properties of Special Parallelograms
Use the information in the diagram to name the special quadrilateral. Example 2 Identify Special Quadrilaterals 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.
Now You Try 2. rhombus ANSWER 3. square ANSWER Identify Special Quadrilaterals Use the information in the diagram to name the special quadrilateral.
SOLUTION By Theorem 6.10, the diagonals of a rhombus are perpendicular. Therefore, BECis a right angle, so ∆BEC is a right triangle. Example 3 Use Diagonals of a Rhombus ABCDis a rhombus. Find the value ofx. By the Corollary to the Triangle Sum Theorem, the acute angles of a right triangle are complementary. So, x = 90 – 60 = 30.
a. You nail four pieces of wood together to build a four-sided frame, as shown. What is the shape of the frame? b. The diagonals measure 7 ft 4 in. and 7 ft 2 in. Is the frame a rectangle? b. The frame is not a rectangle because the diagonals are not congruent. Example 4 Use Diagonals of a Rectangle SOLUTION a. The frame is a parallelogram because both pairs of opposite sides are congruent.
Now You Try 90 ANSWER 12 ANSWER 45 ANSWER Use Diagonals Find the value of x. 4. rhombusABCD 5. rectangleEFGH 6. squareJKLM
Now You Try 19. A B ABCD is a square find x 5x D C