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Concept 1

Concept 1. Concept 2. A. CONSTRUCTION In suppose m  B = 32, CD = 80 inches, BC = 15 inches. Find AD. Use Properties of Parallelograms. Example 1A. AD = BC Opposite sides of a are . Use Properties of Parallelograms. = 15 Substitution.

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Concept 1

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  1. Concept 1

  2. Concept 2

  3. A. CONSTRUCTION In suppose mB = 32, CD = 80 inches, BC = 15 inches. Find AD. Use Properties of Parallelograms Example 1A

  4. AD = BC Opposite sides of a are . Use Properties of Parallelograms = 15 Substitution Answer:AD = 15 inches Example 1

  5. B. CONSTRUCTION In suppose mB = 32, CD = 80 inches, BC = 15 inches. Find mC. Use Properties of Parallelograms Example 1B

  6. mC + mB = 180 Cons. s in a are supplementary. Use Properties of Parallelograms mC + 32= 180 Substitution mC = 148 Subtract 32 from each side. Answer:mC = 148 Example 1

  7. C. CONSTRUCTION In suppose mB = 32, CD = 80 inches, BC = 15 inches. Find mD. Use Properties of Parallelograms Example 1C

  8. mD = mB Opp. s of a are . Use Properties of Parallelograms = 32 Substitution Answer:mD = 32 Example 1

  9. A B C D A. ABCD is a parallelogram. Find AB. A. 10 B. 20 C. 30 D. 50 Example 1A

  10. A B C D B. ABCD is a parallelogram. Find mC. A. 36 B. 54 C. 144 D. 154 Example 1B

  11. A B C D C. ABCD is a parallelogram. Find mD. A. 36 B. 54 C. 144 D. 154 Example 1C

  12. Concept 3

  13. Use Properties of Parallelograms and Algebra A. If WXYZ is a parallelogram, find the value of r. Opposite sides of a parallelogram are . Definition of congruence Substitution Divide each side by 4. Answer:r = 4.5 Example 2A

  14. 8s = 7s + 3 Diagonals of a bisect each other. Use Properties of Parallelograms and Algebra B. If WXYZ is a parallelogram, find the value of s. s = 3 Subtract 7s from each side. Answer:s = 3 Example 2B

  15. Use Properties of Parallelograms and Algebra C. If WXYZ is a parallelogram, find the value of t. ΔWXY  ΔYZW Diagonal separates a parallelogram into 2  triangles. YWX  WYZ CPCTC mYWX = mWYZ Definition of congruence Example 2C

  16. Use Properties of Parallelograms and Algebra 2t = 18 Substitution t = 9 Divide each side by 2. Answer:t = 9 Example 2C

  17. A B C D A. If ABCD is a parallelogram, find the value of x. A. 2 B. 3 C. 5 D. 7 Example 2A

  18. A B C D B. If ABCD is a parallelogram, find the value of p. A. 4 B. 8 C. 10 D. 11 Example 2B

  19. A B C D C. If ABCD is a parallelogram, find the value of k. A. 4 B. 5 C. 6 D. 7 Example 2C

  20. Midpoint Formula Find the midpoint of Since the diagonals of a parallelogram bisect each other, the intersection point is the midpoint of Parallelograms and Coordinate Geometry What are the coordinates of the intersection of the diagonals of parallelogram MNPR, with vertices M(–3, 0), N(–1, 3), P(5, 4), and R(3, 1)? Example 3

  21. Parallelograms and Coordinate Geometry Answer: The coordinates of the intersection of the diagonals of parallelogram MNPR are (1, 2). Example 3

  22. A B C D A. B. C. D. What are the coordinates of the intersection of the diagonals of parallelogram LMNO, with verticesL(0, –3), M(–2, 1), N(1, 5), O(3, 1)? Example 3

  23. Given: are diagonals, and point P is the intersection of Prove:AC and BD bisect each other. Proof: ABCD is a parallelogram and AC and BD are diagonals; therefore, AB║DC and AC is a transversal. BAC  DCA and ABD  CDB by Theorem 3.2. ΔAPBΔCPD by ASA. So, by the properties of congruent triangles BP DPand AP  CP. Therefore, AC and BD bisect each other. Proofs Using the Properties of Parallelograms Write a paragraph proof. Example 4

  24. A B C D Given:LMNO, LN and MO are diagonals and point Q is the intersection of LN and MO. A.LO  MN B.LM║NO C.OQ  QM D.Q is the midpoint of LN. To complete the proof below, which of the following is relevant information? Prove:LNO  NLM Example 4

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