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5.5 Properties of Quadrilaterals

I can identify properties of quadrilaterals. Day 5. Pick up a Quadrilateral Family Tree. Write the name of each quadrilateral inside the figure. Write the definition of each quadrilateral next to the word “definition” In your bell ringer box, write “See Family Tree”.

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5.5 Properties of Quadrilaterals

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  1. I can identify properties of quadrilaterals Day 5 • Pick up a Quadrilateral Family Tree. • Write the name of each quadrilateral inside the figure. • Write the definition of each quadrilateral next to the word “definition” • In your bell ringer box, write “See Family Tree” 5.5 Properties of Quadrilaterals

  2. After studying this section: • You will be able to identify and apply some: • Properties of Parallelograms • Properties of Rectangles • Properties of Kites • Properties of Rhombuses • Properties of Squares • Properties of Isosceles Trapezoids

  3. Properties of Parallelograms: In a parallelogram: • Opposite sides are parallel • Opposite sides are congruent • Opposites angles are congruent • Diagonals bisect each other • All pairs of consecutive angles are supplementary y x x y

  4. Properties of Rectangles: But wait! There’s MORE!!! In a rectangle: • Opposite sides are parallel • Opposite sides are congruent • Opposites angles are congruent • Diagonals bisect each other • All pairs of consecutive angles are supplementary x y x y

  5. Properties of Rectangles: In a rectangle: • All the properties of Parallelograms apply AND • All angles are RIGHT ANGLES • Diagonals are CONGRUENT

  6. Properties of Kites K K • In a kite: • Two disjoint pairs of consecutive sides are congruent • One diagonal is  bisector of the other • One diagonal bisects a pair of opposite angles • One pair of opposite angles are congruent E I T T

  7. Properties of Rhombuses • In a rhombus: • All the properties of parallelograms and kites apply • (in fact, the half properties of kites become FULL properties in the rhombus!) • AND • ALL sides are congruent (equilateral) • Diagonals bisect the angles • Diagonals are both perpendicular bisectors • Diagonals divide the rhombus into four congruent triangles • (what type of triangles do you think they are?) • Yes! Right Triangles!

  8. Properties of Squares In a square: All of the properties of the following quadrilaterals apply: * A square is a parallelogrambecause opposite sides are parallel and congruent, * A square is a rectangle because it is a parallelogram with at least one right angle, and * A square is a rhombus because ALL sides are congruent, and the diagonals are perpendicular bisectors of each other and they are also angle bisectors. * The diagonals of a square form 4congruent RIGHT triangles! parallelogram rectangle rhombus (what type of triangles do you think they are?) Hint: Are the diagonals congruent?

  9. Properties of Isosceles Trapezoids • In an isosceles trapezoid: • * The legs are congruent • * The bases are parallel • * The lower base angles are congruent • * The upper base angles are congruent • * The diagonals are congruent • Any lower base angle is supplementary to any upper base angle.

  10. Sample Proof E D C F G A B H Given: ABCD is a parallelogram <GHA = <FEC HB = DE Prove: GH = EF ~ ~ ~

  11. Sample 2 A Z V R Given: VRZA is a parallelogram AV= 2x-4 VR= 3y+5 RZ= 1/2x+8 ZA= y+12 Find the perimeter of VRZA

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