Properties of Special Quadrilaterals

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Presentation transcript:

Properties of Special Quadrilaterals Unit 5 Pg. 304

Quadrilateral A four sided polygon. Property: The sum of the interior angles is 360º.

Parallelogram A quadrilateral with both pairs of opposite sides parallel. Properties: Both pairs of Opposite Sides are Parallel. Both Pairs of Opposite Sides are Congruent. Both Pairs of Opposite Angles are Congruent. Consecutive angles are Supplementary. The Diagonals Bisect each other. The Diagonal cuts it into 2 Congruent Triangles.

Rectangle A parallelogram with 4 Right Angles. Properties: All the properties of a parallelogram. Diagonals are Congruent. Equiangular.

Rhombus A parallelogram with 4 Congruent Sides. Properties: All the properties of a parallelogram. Diagonals are Perpendicular. Diagonals Bisect the pairs of opposite angles. Equilateral.

Square A Rectangle with 4 Congruent Sides A Rhombus with 4 Right Angles. Properties: All the properties of a Rectangle. All the properties of a Rhombus.

Examples Sometimes, Always, Never???? 1. A rectangle is a square. 2. A square is a rhombus. 3. A rhombus is a rectangle. 4. A parallelogram is a rectangle.

5. QRST is a square. What do you know about it? a. b. c. d. e. f.

EK_____ GK_____ FH_____ 6. EFGH is a rectangle. K is the midpoint of FH. IF EG = 28, what is EK? GK? FH? EK_____ GK_____ FH_____ E F K H G

7. The m<B = 8x+26. Find the value of x. 8. AC = 6x + 24, BD = 8z – 12. Find z. Find the length of AC and BD. z=_____ AC_____ BD_____ B D C

PQRS is a rhombus. 9. Find the value of y. 10. Find the value of x. 11. Find the value of z. P Q 120º 2y + 3 xº 3zº S R 5y - 6

Find the indicated measure. 12. JL _____ 13. MT _____ K JKLM is a rhombus Find the indicated measure. 12. JL _____ 13. MT _____ 14. m<JTK _____ 15. x = _____ 65º 2n T 12-n 20 2xº M L

Find the indicated measure. 16. p = _____ 17. TU ____ 18. UW _____ TUVW is a Square Find the indicated measure. 16. p = _____ 17. TU ____ 18. UW _____ 4(p+3) T U W V 24

Solve for x and y in the following parallelograms. 19. 20. 2a + 1 a = ______ b = ______ 7 2b - 3 21 X = ______ Y = ______ 42º 2xº 7yº

Homework Page 319 Numbers 7-14 Page 321 Numbers 2-22 even