Post on 22-Dec-2015
CCSS
Content StandardsG.CO.11 Prove theorems about parallelograms.G.GPE.4 Use coordinates to prove simple geometric theorems algebraically.Mathematical Practices4 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.
VocabularyTheorem 6.3: Parallelogram Property #1If a quadrilateral is a parallelogram, then
its opposite sides are congruent.
VocabularyTheorem 6.4: Parallelogram Property #2If a quadrilateral is a parallelogram, then
its opposite angles are congruent.
VocabularyTheorem 6.5: Parallelogram Property #3If a quadrilateral is a parallelogram, then
its consecutive angles are supplementary.
VocabularyTheorem 6.6: Parallelogram Property #4If a parallelogram has one right angle,
then it has four right angles.
VocabularyTheorem 6.7: Parallelogram Diagonal Property #1
If a quadrilateral is a parallelogram, then its diagonals bisect each other.
VocabularyTheorem 6.8: Parallelogram Diagonal Property #2
If a quadrilateral is a parallelogram, then each diagonal separates the parallelogram into two congruent triangles.
Example 1AUse Properties of Parallelograms
A. CONSTRUCTION In suppose mB = 32, CD = 80 inches, BC = 15 inches. Find AD.
Example 1BUse Properties of Parallelograms
B. CONSTRUCTION In suppose mB = 32, CD = 80 inches, BC = 15 inches. Find mC.
Example 1CUse Properties of Parallelograms
C. CONSTRUCTION In suppose mB = 32, CD = 80 inches, BC = 15 inches. Find mD.
Example 2AUse Properties of Parallelograms and Algebra
A. If WXYZ is a parallelogram, find the value of r.
Example 2BUse Properties of Parallelograms and Algebra
B. If WXYZ is a parallelogram, find the value of s.
Example 2CUse Properties of Parallelograms and Algebra
C. If WXYZ is a parallelogram, find the value of t.
Example 3Parallelograms 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)?