Download presentation

Presentation is loading. Please wait.

Published bySavannah Bushell Modified about 1 year ago

1
Concept 1

2
Concept 2

6
Example 1 Identify Parallelograms Determine whether the quadrilateral is a parallelogram. Justify your answer. Answer:Each pair of opposite sides has the same measure. Therefore, they are congruent. If both pairs of opposite sides of a quadrilateral are congruent, the quadrilateral is a parallelogram.

7
A.A B.B C.C D.D Example 1 A.Both pairs of opp. sides ||. B.Both pairs of opp. sides . C.Both pairs of opp. ’s . D.One pair of opp. sides both || and . Which method would prove the quadrilateral is a parallelogram?

8
Example 2 Use Parallelograms to Prove Relationships MECHANICS Scissor lifts, like the platform lift shown below, are commonly applied to tools intended to lift heavy items. In the diagram, A C and B D. Explain why the consecutive angles will always be supplementary, regardless of the height of the platform.

9
Example 2 Use Parallelograms to Prove Relationships Answer:Since both pairs of opposite angles of quadrilateral ABCD are congruent, ABCD is a parallelogram by Theorem 6.10. Theorem 6.5 states that consecutive angles of parallelograms are supplementary. Therefore, m A + m B = 180 and m C + m D = 180. By substitution, m A + m D = 180 and m C + m B = 180.

10
A.A B.B C.C D.D Example 2 A. A B B. A C C.AB BC D.m A + m C = 180 The diagram shows a car jack used to raise a car from the ground. In the diagram, AD BC and AB DC. Based on this information, which statement will be true, regardless of the height of the car jack.

11
Example 3 Use Parallelograms and Algebra to Find Values Find x and y so that the quadrilateral is a parallelogram. Opposite sides of a parallelogram are congruent.

12
Example 3 Use Parallelograms and Algebra to Find Values Substitution Distributive Property Add 1 to each side. Subtract 3x from each side. AB = DC

13
Example 3 Use Parallelograms and Algebra to Find Values Answer:So, when x = 7 and y = 5, quadrilateral ABCD is a parallelogram. Substitution Distributive Property Add 2 to each side. Subtract 3y from each side.

14
A.A B.B C.C D.D Example 3 A.m = 2 B.m = 3 C.m = 6 D.m = 8 Find m so that the quadrilateral is a parallelogram.

15
Concept 3

16
Example 4 Parallelograms and Coordinate Geometry COORDINATE GEOMETRY Graph quadrilateral QRST with vertices Q(–1, 3), R(3, 1), S(2, –3), and T(–2, –1). Determine whether the quadrilateral is a parallelogram. Justify your answer by using the Slope Formula. If the opposite sides of a quadrilateral are parallel, then it is a parallelogram.

17
Example 4 Parallelograms and Coordinate Geometry Answer:Since opposite sides have the same slope, QR ║ST and RS║TQ. Therefore, QRST is a parallelogram by definition.

18
1.A 2.B Example 4 A.yes B.no Graph quadrilateral EFGH with vertices E(–2, 2), F(2, 0), G(1, –5), and H(–3, –2). Determine whether the quadrilateral is a parallelogram.

19
Example 5 Parallelograms and Coordinate Proofs Write a coordinate proof for the following statement. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. ●Begin by placing the vertex A at the origin. Step 1Position quadrilateral ABCD on the coordinate plane such that AB DC and AD BC. ●Let AB have a length of a units. Then B has coordinates (a, 0).

20
Example 5 Parallelograms and Coordinate Proofs ●So that the distance from D to C is also a units, let the x-coordinate of D be b and of C be b + a. ●Since AD BC position the endpoints of DC so that they have the same y-coordinate, c.

21
Example 5 Parallelograms and Coordinate Proofs Step 2Use your figure to write a proof. Given:quadrilateral ABCD, AB DC, AD BC Prove:ABCD is a parallelogram. Coordinate Proof: By definition a quadrilateral is a parallelogram if opposite sides are parallel. Use the Slope Formula.

22
Example 5 Parallelograms and Coordinate Proofs Answer:So, quadrilateral ABCD is a parallelogram because opposite sides are parallel. Since AB and CD have the same slope and AD and BC have the same slope, AD ║BC and AB║CD. The slope of CD is 0. The slope of AB is 0.

23
1.A 2.B Example 5 Which of the following can be used to prove the statement below? If a quadrilateral is a parallelogram, then one pair of opposite sides is both parallel and congruent. A.AB = a units and DC = a units; slope of AB = 0 and slope of DC = 0 B.AD = c units and BC = c units; slope of and slope of

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google