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Warm Up

Warm Up. A woodworker constructs a rectangular picture frame so that JK = 50 cm and JL = 86 cm. Find HM. A slab of concrete is poured with diagonal spacers. In rectangle CNRT, CN = 35 ft , and NT = 58 ft. Find each length. a) Find TR b) Find CE. Squares and Rhombi. Section 6.4.

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Warm Up

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  1. Warm Up • A woodworker constructs a rectangular picture frame so that JK = 50 cm and JL = 86 cm. Find HM. • A slab of concrete is poured with diagonal spacers. In rectangle CNRT, CN = 35 ft, and NT = 58 ft. Find each length. a) Find TR b) Find CE

  2. Squares and Rhombi Section 6.4

  3. Square • Diagonals are Perpendicular • Diagonals bisect a pair of opposite angles • All sides are congruent • Contains 4 right angles • Diagonals are the same. • Diagonals bisect each other.

  4. Rhombus • Diagonals are perpendicular. • Diagonals bisect a pair of opposite angles. • All sides are congruent. • Diagonals are not the same. • Diagonals bisect each other.

  5. Name all Quadrilaterals with these properties: • 1. all angles are congruent • 2. all sides are congruent • 3. diagonals are congruent • 4. Two pairs of opposite sides are congruent and parallel • 5. All sides and all angles are congruent • 6. The diagonals are perpendicular

  6. Use rhombus ABCD to find each • 1. If m∠BAF = 28. Find all missing angles.

  7. 2. Find x if m∠AFB = 16x + 6.

  8. 3. If m∠ACD = 36. Find m∠ABC.

  9. 4. Find x if m∠BFC= 120 – 4x.

  10. 5. AF= 3, AD = 5, find DF.

  11. 1. If m∠RST = 67. Find all missing angles.

  12. 2. Find all missing angles if m∠STV = 135.

  13. 3. If m∠SWT = 2x + 8. Find x.

  14. 4. If m∠WRV = 5x +5 and m∠WRS = 7x – 19. Find x.

  15. True or False • 1. Every square is a rhombus. • 2. Every rhombus is a square. • 3. Every rectangle is a square. • 4. Every square is a rectangle. • 5. All rhombi are parallelograms. • 6. Every parallelogram is a rectangle.

  16. ABCD is a square. 1. m⦟ABD = 5x + 5. Find x. A B C D

  17. ABCD is a square. 2. If BD = 10 inches, what does AB measure?

  18. Lesson Quiz: PQRS is a rhombus. Find each measure. 1.QP2. mQRP

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