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

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

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

Parallelogram A quadrilateral with two pairs of parallel sides

1. T RAPEZOID 1. Four-sided polygon QUADRILATERAL P ARALLELOGRAM S QUARE K ITE I SOSCELES T RAPEZOID

Parallelogram – How can we construct a parallelogram?

Parallelogram

1 2

1 2

The two triangles formed by a diagonal are congruent by ASA.

Parallelogram What does that mean about opposite sides of a parallelogram?

Parallelogram What does that mean about opposite sides of a parallelogram? CPCTC

1. TRAPEZOID 1. Four-sided polygon Q UADRILATERAL PARALLELOGRAM S QUARE R ECTANGLE R HOMBUS K ITE I SOSCELES T RAPEZOID

1. 1. Four-sided polygon QUADRILATERAL P ARALLELOGRAM S QUARE Opposite sides are congruent

Parallelograms What about opposite angles in a parallelogram?

1. 1. Four-sided polygon QUADRILATERAL 2. Opposite angles are congruent P ARALLELOGRAM S QUARE Opposite sides are congruent

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

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

1. 1. Four-sided polygon QUADRILATERAL 2. Opposite angles are congruent 3. Diagonals bisect each other 4. P ARALLELOGRAM S QUARE Opposite sides are congruent

Parallelogram 5 6 What kind of angles are angles 5 & 6?

Consecutive angles in a parallelogram are supplementary. Parallelogram 5 6

1. 1. Four-sided polygon QUADRILATERAL 2. Opposite angles are congruent 3. Diagonals bisect each other 4. Consecutive angles are supp. P ARALLELOGRAM S QUARE Opposite sides are congruent

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

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

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

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

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

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

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