6.2 Parallelograms.

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Presentation transcript:

6.2 Parallelograms

CCSS Content Standards G.CO.11 Prove theorems about parallelograms. G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. Mathematical Practices 4 Model with mathematics. 3 Construct viable arguments and critique the reasoning of others.

Then/Now You classified polygons with four sides as quadrilaterals. Recognize and apply properties of the sides and angles of parallelograms. Recognize and apply properties of the diagonals of parallelograms.

Vocabulary Parallelogram: a quadrilateral with both pairs of opposite sides parallel

Vocabulary Theorem 6.3: Parallelogram Property #1 If a quadrilateral is a parallelogram, then its opposite sides are congruent.

Vocabulary Theorem 6.4: Parallelogram Property #2 If a quadrilateral is a parallelogram, then its opposite angles are congruent.

Vocabulary Theorem 6.5: Parallelogram Property #3 If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

Vocabulary Theorem 6.6: Parallelogram Property #4 If a parallelogram has one right angle, then it has four right angles.

Vocabulary Theorem 6.7: Parallelogram Diagonal Property #1 If a quadrilateral is a parallelogram, then its diagonals bisect each other.

Vocabulary Theorem 6.8: Parallelogram Diagonal Property #2 If a quadrilateral is a parallelogram, then each diagonal separates the parallelogram into two congruent triangles.

Parallelogram Mark in all of the sides and angles

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

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

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

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

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

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

Example 2A A. If WXYZ is a parallelogram, find the value of r. Use Properties of Parallelograms and Algebra A. If WXYZ is a parallelogram, find the value of r.

Example 2B B. If WXYZ is a parallelogram, find the value of s. Use Properties of Parallelograms and Algebra B. If WXYZ is a parallelogram, find the value of s.

Example 2C C. If WXYZ is a parallelogram, find the value of t. Use Properties of Parallelograms and Algebra C. If WXYZ is a parallelogram, find the value of t.

Example 2A A. If ABCD is a parallelogram, find the value of x. A. 2

Example 2B B. If ABCD is a parallelogram, find the value of p. A. 4

Example 2C C. If ABCD is a parallelogram, find the value of k. A. 4

Example 3 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 Parallelograms and Coordinate Geometry What are the coordinates of the intersection of the diagonals of parallelogram LMNO, with vertices L(0, –3), M(–2, 1), N(1, 5), O(3, 1)?