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Bell Ringer

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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Bell Ringer

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  1. Bell Ringer

  2. Rhombus, Rectangles, and Squares

  3. 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

  4. 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 mA = mB = mC = mD = 90°. Example 1 Use Properties of Special Parallelograms In the diagram, ABCDis a rectangle. a. Find ADand AB. b. Find mA, mB, mC, and mD.

  5. 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

  6. 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.

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

  8. 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.

  9. 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.

  10. Now You Try  90 ANSWER 12 ANSWER 45 ANSWER Use Diagonals Find the value of x. 4. rhombusABCD 5. rectangleEFGH 6. squareJKLM

  11. Now You Try 

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  15. Now You Try 

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

  17. Page 328

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

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