Download presentation

Presentation is loading. Please wait.

Published byJoshua Newman Modified over 3 years ago

1
**Recall Theorem 6-3 The diagonals of a parallelogram bisect each other.**

Section 6-3 Prove that Quadrilateral is a Parallelogram SPI 32 H: apply properties of quadrilaterals to solve a real-world problem Objectives: Determine whether a quadrilateral is a parallelogram Recall Theorem 6-3 The diagonals of a parallelogram bisect each other.

2
**If a diagram shows two diagonals bisect then it is a parallelogram.**

Theorem 6-5 Converse of Theorem 6-3 If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. If a diagram shows two diagonals bisect then it is a parallelogram.

3
Theorem 6-6 If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.

4
**Use Theorems to Solve Problems**

Find values of x and y for which ABCD must be a parallelogram. If the diagonals of quadrilateral ABCD bisect each other, then ABCD is a parallelogram by Theorem 6-5. Write and solve two equations to find values of x and y for which the diagonals bisect each other. 10x – 24 = 8x Diagonals of parallelograms 2y – 80 = y + 9 bisect each other. 2x – 24 = y – 80 = 9 Collect the variable terms on one side. x = 18 2x = 36 y = 89 Solve. If x = 18 and y = 89, then ABCD is a parallelogram.

5
Theorem 6-7 If both pairs of opposite sides of a quadrilateral are congruent, the quadrilateral is a parallelogram.

6
Theorem 6-8 If both pairs of opposite angles of a quadrilateral are congruent, the quadrilateral is a parallelogram.

7
**Use Theorems to Solve Problems**

Determine whether the quadrilateral is a parallelogram. Explain. a. a. All you know about the quadrilateral is that only one pair of opposite sides is congruent. Therefore, you cannot conclude that the quadrilateral is a parallelogram. b. b. The sum of the measures of the angles of a polygon is (n – 2)180, where n represents the number of sides, so the sum of the measures of the angles of a quadrilateral is (4 – 2)180 = 360. If x represents the measure of the unmarked angle, x = 360, so x = 105. Theorem 6-8 states If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Because both pairs of opposite angles are congruent, the quadrilateral is a parallelogram by Theorem 6-8.

8
**Parallelograms and Real-world**

Dallas Center Waterfront Park in Vancouver B.C.

Similar presentations

OK

Ways of proving a quadrilaterals are parallelograms Section 5-2.

Ways of proving a quadrilaterals are parallelograms Section 5-2.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on different occupations in nursing Ppt on shell scripting language Training ppt on personality development Simple ppt on fossil fuel for students Ppt on pizza hut in india Ppt on object-oriented programming concepts in c++ Ppt on condition monitoring Ppt on topic why do we fall ill Ppt on child labour free download in hindi Ppt on 3d geometry maths class 11