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6-4: Properties of Special Parallelograms

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Presentation on theme: "6-4: Properties of Special Parallelograms"— Presentation transcript:

1 6-4: Properties of Special Parallelograms
Page 395 15) 82.9 16) 110 17) 18) 50° 19) 130° 20) 21) 10 22) 20 23) 28 24) 14 32) ∠𝑹𝑲𝑴 33) ∠𝑲𝑴𝑷 34) 𝑹𝑻 35) 𝑲𝑴 36) 𝑹𝑲 37) 𝑹𝑷 38) ∠𝑹𝑲𝑷 39) ∠𝑹𝑻𝑷 40) 180° 41) x = 119, y = 61, z = 119 42) x = 90, y = 37, z = 53 43) x = 24, y = 50, z = 50 46) x = 3, y = 6 47) x = 5, y = 8 11/29/2018 4:40 AM 6-4: Properties of Special Parallelograms

2 6-4: Properties of Special Parallelograms
Page 402 11) Yes, all sides are congruent to each other 12) Yes, Each pair of angles are alternate interior angles 13) No 14) JK and LM’s Slope is –7/2; KL and MJ = -1/5 15) JK and LM’s Slope is –7/2; KL and MJ = −1/5 20) A = 16, b = 14 21) A = 16.5, b = 23.2 22) A = 7.25, b = 6.5 23) A = 8.4, b = 20 11/29/2018 4:40 AM 6-4: Properties of Special Parallelograms

3 6-4: Properties of Special Parallelograms

4 Properties of Special Parallelograms
Section 6-4 Geometry PreAP, Revised ©2013 11/29/2018 4:40 AM 6-4: Properties of Special Parallelograms

5 Properties of Rectangles
If a quadrilateral is a rectangle, then it is a parallelogram If a parallelogram is a rectangle, then its diagonals are congruent 11/29/2018 4:40 AM 6-4: Properties of Special Parallelograms

6 6-4: Properties of Special Parallelograms
Rhombus A. A rhombus is another special quadrilateral. A rhombus is a quadrilateral with four congruent sides. 11/29/2018 4:40 AM 6-4: Properties of Special Parallelograms

7 6-4: Properties of Special Parallelograms
Properties of Rhombus If a quadrilateral is a rhombus, then it is a parallelogram If a parallelogram is a rhombus, then its diagonals are perpendicular If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles 11/29/2018 4:40 AM 6-4: Properties of Special Parallelograms

8 6-4: Properties of Special Parallelograms
Rhombus A. A rhombus is another special quadrilateral. A rhombus is a quadrilateral with four congruent sides. 11/29/2018 4:40 AM 6-4: Properties of Special Parallelograms

9 6-4: Properties of Special Parallelograms
Squares A square is a regular parallelogram. All angles are congruent All sides are congruent 11/29/2018 4:40 AM 6-4: Properties of Special Parallelograms

10 6-4: Properties of Special Parallelograms
Shapes 11/29/2018 4:40 AM 6-4: Properties of Special Parallelograms

11 6-4: Properties of Special Parallelograms
Example 1 TVWX is a rhombus. Find TV. 11/29/2018 4:40 AM 6-4: Properties of Special Parallelograms

12 6-4: Properties of Special Parallelograms
Example 2 CDFG is a rhombus. Solve for mGCH if mGCD = (b + 3)° and mCDF = (6b – 40)° 11/29/2018 4:40 AM 6-4: Properties of Special Parallelograms

13 6-4: Properties of Special Parallelograms
Your Turn Find the length of diagonal in a rectangle of ABCD if AC = 2(5a + 1) and BD = 2(a + 1). 11/29/2018 4:40 AM 6-4: Properties of Special Parallelograms

14 6-4: Properties of Special Parallelograms
Example 3 In the figure, a small square is inside a larger square. What is the area, in terms of x, of the shaded region? 11/29/2018 4:40 AM 6-4: Properties of Special Parallelograms

15 6-4: Properties of Special Parallelograms
Assignment Pg 412: 10-15, all 11/29/2018 4:40 AM 6-4: Properties of Special Parallelograms


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