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Prove and apply properties of parallelograms. Use properties of parallelograms to solve problems.

Objectives. Prove and apply properties of parallelograms. Use properties of parallelograms to solve problems. _________________ - A quadrilateral with two pairs of parallel sides. In CDEF , DE = 74 mm, DG = 31 mm, and m  FCD = 42° . Find CF.

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Prove and apply properties of parallelograms. Use properties of parallelograms to solve problems.

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  1. Objectives Prove and apply properties of parallelograms. Use properties of parallelograms to solve problems.

  2. _________________ - A quadrilateral with two pairs of parallel sides.

  3. In CDEF, DE = 74 mm, DG = 31 mm, and mFCD = 42°. Find CF. Example 1A: Properties of Parallelograms

  4. In CDEF, DE = 74 mm, DG = 31 mm, and mFCD = 42°. Find mEFC. Example 1B: Properties of Parallelograms

  5. In CDEF, DE = 74 mm, DG = 31 mm, and mFCD = 42°. Find DF. Example 1C: Properties of Parallelograms

  6. Example 2A: Using Properties of Parallelograms to Find Measures WXYZ is a parallelogram. Find mZ.

  7. Example 2B EFGH is a parallelogram. Find JG.

  8. L K J Example 3: Parallelograms in the Coordinate Plane Three vertices of JKLM are J(3, –8), K(–2, 2), and L(2, 6). Find the coordinates of vertex M. Since JKLM is a parallelogram, both pairs of opposite sides must be parallel. Step 1 Graph the given points.

  9. Step 2 Find the slope of by counting the units from K to L. L K J Example 3 Continued Step 3 Start at J and count the same number of units. M

  10. Step 4 Use the slope formula to verify that L K M J Example 3 Continued

  11. Q S P Example 3B Three vertices of PQRS are P(–3, –2), Q(–1, 4), and S(5, 0). Find the coordinates of vertex R. Since PQRS is a parallelogram, both pairs of opposite sides must be parallel. Step 1 Graph the given points.

  12. Step 2 Find the slope of by counting the units from P to Q. Q S P Example 3B Continued R Step 3 Start at S and count the same number of units.

  13. Step 4 Use the slope formula to verify that R Q S P Example 3B Continued

  14. Example 4A: Using Properties of Parallelograms in a Proof Write a two-column proof. Given: ABCD is a parallelogram. Prove:∆AEB∆CED

  15. Example 4A Continued Proof: 1. 1. 2. 3. 4.

  16. Example 4B: Using Properties of Parallelograms in a Proof Write a two-column proof. Given: GHJN and JKLM are parallelograms. H and M are collinear. N and K are collinear. Prove:H M

  17. 2. Example 4B Continued Proof: 1. 1. 2. 3. 3. 4. 4.

  18. Example 4C Write a two-column proof. Given: GHJN and JKLM are parallelograms. H and M are collinear. N and K are collinear. Prove: N  K

  19. 2. Example 4C Continued Proof: 1. 1. 2. 3. 3. 4. 4.

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