Warm Up Create an octagon inscribed in a circle.

Parallelograms Essential Question: How do you find missing segment lengths and angles of parallelograms? Assessment: Students will demonstrate in writing on their homework worksheet.

What is a Parallelogram? A parallelogram is a quadrilateral in which opposite sides are parallel. EQ: How do you find missing segment lengths and angles of parallelograms? A: Students will demonstrate in writing on their homework worksheet.

Properties of a Parallelogram EQ: How do you find missing segment lengths and angles of parallelograms?

Properties of a Parallelogram (cont.) Consecutive angles are supplementary. ∠ A + ∠ D = 180⁰ ∠ B + ∠ C = 180⁰ The diagonals bisect one another. EQ: How do you find missing segment lengths and angles of parallelograms? A: Students will demonstrate in writing on their homework worksheet.

Example #1 Given: Quadrilateral ABCD is a parallelogram Prove: ∠ BAD ≅ ∠ BCD ∠ ABC ≅ ∠ ADC StatementReason ∠ BAD ≅ ∠ ADX ∠ ABC ≅ ∠ YAB ∠ ADX ≅ ∠ BCD ∠ YAB ≅ ∠ ADC Transitive Property EQ: How do you find missing segment lengths and angles of parallelograms? A: Students will demonstrate in writing on their homework worksheet. Quadrilateral ABCD is a parallelogram Given Opposite Angles Corresponding Angles ∠ BAD ≅ ∠ BCD ∠ ABC ≅ ∠ ADC

Example 2 A parallelogram is shown below. Which angles and sides must be congruent to each other? Select all that apply. A)MN ≅ NP B)MN ≅ OP C)MO ≅ NP D) ∠ M ≅ ∠ O E) ∠ N ≅ ∠ P F) ∠ M ≅ ∠ P EQ: How do you find missing segment lengths and angles of parallelograms? A: Students will demonstrate in writing on their homework worksheet.

Example 3 The parallelogram ABCE has diagonals AC and EB that intersect at point D. A proof that the diagonals of a parallelogram bisect each other is shown below. Fill in the missing statement and reason. STATEMENTSREASONS ABCE is a parallelogramGiven AC and EB are diagonals of the parallelogram Given ∠BEC ≅ ∠EBA ∠BAC ≅ ∠ACE AB ≅ EC Opposite sides of a parallelogram are congruent. ∆ABD ≅ ∆CED Angle – Side – Angle Congruence Postulate AD ≅ DC ED ≅ DB Corresponding parts of a congruent triangle are congruent. EQ: How do you find missing segment lengths and angles of parallelograms? Alt. Int. Angles

Examples Find the measurement indicated in each parallelogram EQ: How do you find missing segment lengths and angles of parallelograms? A: Students will demonstrate in writing on their homework worksheet.