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6.2 Parallelograms
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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.
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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.
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Vocabulary Parallelogram:
a quadrilateral with both pairs of opposite sides parallel
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Vocabulary Theorem 6.3: Parallelogram Property #1
If a quadrilateral is a parallelogram, then its opposite sides are congruent.
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Vocabulary Theorem 6.4: Parallelogram Property #2
If a quadrilateral is a parallelogram, then its opposite angles are congruent.
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Vocabulary Theorem 6.5: Parallelogram Property #3
If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.
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Vocabulary Theorem 6.6: Parallelogram Property #4
If a parallelogram has one right angle, then it has four right angles.
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Vocabulary Theorem 6.7: Parallelogram Diagonal Property #1
If a quadrilateral is a parallelogram, then its diagonals bisect each other.
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Vocabulary Theorem 6.8: Parallelogram Diagonal Property #2
If a quadrilateral is a parallelogram, then each diagonal separates the parallelogram into two congruent triangles.
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Parallelogram Mark in all of the sides and angles
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Example 1A A. ABCD is a parallelogram. Find AB. A. 10 B. 20 C. 30
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Example 1B B. ABCD is a parallelogram. Find mC. A. 36 B. 54 C. 144
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Example 1C C. ABCD is a parallelogram. Find mD. A. 36 B. 54 C. 144
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Example 1A Use Properties of Parallelograms A. CONSTRUCTION In suppose mB = 32, CD = 80 inches, BC = 15 inches. Find AD.
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Example 1B Use Properties of Parallelograms B. CONSTRUCTION In suppose mB = 32, CD = 80 inches, BC = 15 inches. Find mC.
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Example 1C Use Properties of Parallelograms C. CONSTRUCTION In suppose mB = 32, CD = 80 inches, BC = 15 inches. Find mD.
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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.
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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.
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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.
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Example 2A A. If ABCD is a parallelogram, find the value of x. A. 2
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Example 2B B. If ABCD is a parallelogram, find the value of p. A. 4
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Example 2C C. If ABCD is a parallelogram, find the value of k. A. 4
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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)?
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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)?
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