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The Quadrilateral Family Tree

The Quadrilateral Family Tree. Parallelograms I can use the properties of a parallelogram to solve problems. ________________________. 1. _____________________. __________. _____________________. 1. _____________________. _____________________. 1. _____________________.

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The Quadrilateral Family Tree

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  1. The Quadrilateral Family Tree Parallelograms I can use the properties of a parallelogram to solve problems.

  2. ________________________ 1. _____________________ __________ _____________________ 1. _____________________ _____________________ 1. _____________________ 2. _____________________ 1. _____________________ 2. _____________________ 3. _______________ 3. _____________________ 4. _____________________ __________________ _____________________ 1. _____________________ _____________________ 1. _____________________ 2. _____________________ 1. _____________________ 2. _____________________ 3. _____________________ 2. _____________________ 3. _____________________ 3. _____________________ 4. _____________________ _____________________ 1. _____________________ 2. _____________________

  3. Quadrilateral __________ _____________________ 1. _____________________ _____________________ 1. _____________________ 2. _____________________ 1. _____________________ 2. _____________________ 3. _______________ 3. _____________________ 4. _____________________ __________________ _____________________ 1. _____________________ _____________________ 1. _____________________ 2. _____________________ 1. _____________________ 2. _____________________ 3. _____________________ 2. _____________________ 3. _____________________ 3. _____________________ 4. _____________________ _____________________ 1. _____________________ 2. _____________________ 1. Four-sided polygon

  4. Parallelograms

  5. Parallelogram • A quadrilateral with two pairs of parallel sides

  6. QUADRILATERAL 1. Four-sided polygon Kite Trapezoid 1. Parallelogram 1. 1. 2. 2. 3. 3. 4. Isosceles Trapezoid 1. 1. 1. 2. 2. 3. 2. 3. 4. 3. Square 1. 2.

  7. Parallelogram – How can we construct a parallelogram?

  8. Parallelogram

  9. Parallelogram 2 1

  10. Parallelogram 2 1

  11. Parallelogram 3 2 1 4

  12. Parallelogram 3 2 1 4

  13. Parallelogram 3 2 1 4

  14. Parallelogram 3 2 1 4

  15. 3 2 1 4 Parallelogram • The two triangles formed by a diagonal are congruent by ASA.

  16. Parallelogram • What does that mean about opposite sides of a parallelogram? 3 2 1 4

  17. Parallelogram • What does that mean about opposite sides of a parallelogram? 3 2 1 4 CPCTC

  18. Quadrilateral 1. Four-sided polygon Kite TRAPEZOID 1. PARALLELOGRAM 1. 1. 2. 2. 3. 3. 4. Isosceles Trapezoid Rhombus 1. Rectangle 1. 1. 2. 2. 3. 2. 3. 4. 3. Square 1. 2.

  19. QUADRILATERAL 1. Four-sided polygon Parallelogram 1. 2. 3. 4. 1. 1. 1. 2. 2. 3. 2. 3. 4. 3. Square 1. 2. 1. 2. 1. Opposite sides are congruent 3.

  20. Parallelograms • What about opposite angles in a parallelogram?

  21. QUADRILATERAL 1. Four-sided polygon Parallelogram 1. 2. Opposite angles are congruent 3. 4. 1. 1. 1. 2. 2. 3. 2. 3. 4. 3. Square 1. 2. 1. 2. 1. Opposite sides are congruent 3.

  22. Parallelograms • Are these two triangles congruent? By which postulate? 2 1

  23. Parallelogram • Since the triangles are congruent, the diagonals of the parallelogram bisect each other.

  24. QUADRILATERAL 1. Four-sided polygon Parallelogram 1. 2. Opposite angles are congruent 3. Diagonals bisect each other 4. 1. 1. 1. 2. 2. 3. 2. 3. 4. 3. Square 1. 2. 1. 2. 1. Opposite sides are congruent 3.

  25. Parallelogram • What kind of angles are angles 5 & 6? 5 6

  26. Parallelogram • Consecutive angles in a parallelogram are supplementary. 5 6

  27. QUADRILATERAL 1. Four-sided polygon Parallelogram 1. 2. Opposite angles are congruent 3. Diagonals bisect each other 4. Consecutive angles are supp. 1. 1. 1. 2. 2. 3. 2. 3. 4. 3. Square 1. 2. 1. 2. 1. Opposite sides are congruent 3.

  28. In CDEF, DE = 74 mm, DG = 31 mm, and mFCD = 42°. Find CF. Find mEFC. Find DF. opp. sides cons. s supp. diags. bisect each other. Example CF = 74 mm mEFC + mFCD= 180° mEFC= 138° DF = 2DG DF = 62

  29. opp. sides opp. s  diags. bisect each other. Your Turn In KLMN, LM = 28 in., LN = 26 in., and mLKN= 74°. Find KN. Find mNML. Find LO. LM = 28 in. NML  LKN mNML= 74° LN = 2LO LO = 13 in.

  30. Example WXYZ is a parallelogram. Find YZ. YZ = 52

  31. Example WXYZ is a parallelogram. Find mZ. mZ= 65°

  32. Example EFGH is a parallelogram. Find JG. JG = 12

  33. Your Turn EFGH is a parallelogram. Find FH. FH = 18

  34. Lesson Quiz In PNWL, NW = 12, PM = 9, and mWLP= 144°. 1.PW 2.mPNW 18 144° QRST is a parallelogram. Find each measure. 3.TQ *4. mT 28 71°

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