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6.2 Parallelograms.

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Presentation on theme: "6.2 Parallelograms."— Presentation transcript:

1 6.2 Parallelograms

2 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.

3 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.

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

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

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

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

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

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

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

11 Parallelogram Mark in all of the sides and angles

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

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

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

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

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

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

18 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.

19 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.

20 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.

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

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

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

24 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)?

25 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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