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Proving Quadrilaterals 4.5

Proving Quadrilaterals 4.5. homework. Remember and apply properties of quadrilaterals to find missing information. Write Proofs with Quadrilaterals. homework. homework. homework. homework. homework. In parallelogram JKLM , m  MLK = 60°. Find each indicated value, state why. 60 .

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Proving Quadrilaterals 4.5

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  1. Proving Quadrilaterals 4.5

  2. homework • Remember and apply properties of quadrilaterals to find missing information. • Write Proofs with Quadrilaterals

  3. homework

  4. homework

  5. homework

  6. homework

  7. homework In parallelogram JKLM, mMLK = 60°. Find each indicated value, state why. 60 d. y c. mJKL b. mMJK a. x y = 3 mJKL = 120 x = 7 mMJK = 60 a. Opposite sides are congruent. b. Opposite angles are congruent. d. Diagonals bisect each other. c. Consecutive angles are supplementary.

  8. PQRS is a parallelogram. Complete each statement. Consecutive angles are supplementary, so x = 24. Opposite sides are congruent, so y = 3. Diagonals bisect each other, so z = 1.5. Opposite angles are congruent, so w = 5 (Explanation follows).

  9. First term –15 1 Numbers that Multiply to be –15 and add to be –14 3w² + 3 = 14w + 8 AC = –15 B = –14 3w² – 14w – 5 = 0 3w 3w Simplify. (w – 5)(3w + 1) = 0 w = 5 or w = – ⅓

  10. 65 d. mEDG =65 Find mDEG homework CDEF is a rhombus. Find each indicated value, state why. c. mDGE b. y a. x mDGE = 90 mDEG = 25 x = 7 y = 1 c. Diagonals are perpendicular. a. All sides are congruent. b. Diagonals bisect each other. d. Triangle sum to 180.

  11. homework LMNP is a square. Complete each statement. All sides are congruent, so x = 3. Diagonals bisect each other, so y = .5. Diagonals are congruent, so z = 4. Diagonal are perpendicular so mLQP = 90. Diagonal bisect vertices angles so mQLP = 45.

  12. homework Use the parallelogram labeled as shown at right. Find each indicated measure. (not drawn to scale) t = 5 MN = 10 x = 15 NP = 15 x = 30 mMNP = 150 NS = 35 mM = 70 x = 5 mMNS = 35 NP = 20 mMNP = 100 x = 20 NS = 5 mM = 20

  13. 2.JM || KL 4.JK || ML homework Given:J is supplementary to K & M Prove:JKLM is a Parallelogram 1.Given 1. J is supplementary to K • Converse Consecutive Int. ’s are Supplementary 3.J is supplementary to M 3.Given 4. Converse Consecutive Int. ’s are Supplementary 5.JKLM is a Parallelogram 5.Definition of Parallelogram

  14. 2.Construct PR homework Given:PQRS is a parallelogram Prove:PQ  SR QR  PS 1 2 3 4 1. PQRS is a parallelogram 1.Given 2.Segment Construction 3.3  2 3.Alternate Interior Angles 4.4  1 4.Alternate Interior Angles 5. PQR   RSP 5. ASA 6. PQ  SR; QR  PS 6.CPCTC

  15. DEFG is a Rhombus DEFG is a Rhombus 1. 2. DEEFFGGD 3. EG  EG homework Given: Prove:D  F home 1. Given 2. Definition of Rhombus 3. Reflexive 4. SSS 4. ∆GDE  ∆GFE 5. D  F 5. CPCTC

  16. Assignment Geometry: 4.5A and 4.5B Section 9 – 22

  17. Conditions for Special Quadrilaterals 4.6

  18. homework • Review properties of quadrilaterals.

  19. homework

  20. homework

  21. homework

  22. Assignment Geometry: Quadrilaterals and Algebra

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