6-1 Classifying Quadrilaterals 6-2 Properties of Parallelograms
Special Quadrilaterals A parallelogram is a quadrilateral with both pairs of opposite sides parallel. A rhombus is a parallelogram with four congruent sides. A rectangle is a parallelogram with four right angles. A square is a parallelogram with four congruent sides and four right angles. A kite is a quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent. A trapezoid is a quadrilateral with exactly one pair of parallel sides. An isosceles trapezoid is one with the nonparallel opposite sides congruent.
rectangle parallelogram square isosceles trapezoid trapezoid rhombus quadrilateral
Quadrilateral Family Tree First, my great-great-grandfather, the Quadrilateral, was born. Later, when he grew up, he had twins. Well, not twins exactly. Trapezoid had one pair of sides parallel. Parallelogram had both pairs of sides parallel. My great-grandfather was Parallelogram. He wanted to come to America. The trip was difficult. It changed his shape from to . So he became a Rectangle. Meanwhile, another parallelogram made the same trip to America. The trip was difficult for her too. It changed her shape from to . So she became a Rhombus. So, my father was a Rectangle and my mother was a Rhombus. I got the best traits from each—my father’s right angles and my mother’s congruent sides. As you know, I am a Square . . . and we all lived happily ever after.
Always, Sometimes, Never . . . Answer the following with always, sometimes, or never. Rectangles are squares. Isosceles trapezoids are parallelograms. Trapezoids are isosceles. Rhombuses are quadrilaterals. Kites are parallelograms. Rhombuses are squares. Squares are rectangles. Rectangles are regular quadrilaterals. Parallelograms are squares. Quadrilaterals have four congruent angles. S N A Rectangles are rhombuses. Parallelograms are trapezoids. Trapezoids have both pairs of opposite sides parallel. Trapezoids have a pair of congruent sides. Kites have two pairs of congruent sides. Squares are regular quadrilaterals. Kites have congruent diagonals. Trapezoids have four congruent sides. Parallelograms have four congruent angles. Isosceles trapezoids have one pair of opposite sides congruent. S N A
Coordinate Geometry Determine the most precise name for a quadrilateral ABCD with vertices. Use distance formulas and slope to prove your case. A (3, 3) B (2, 4) C (3, 1) D (2, 2) square
Classifying Quadrilaterals Find the value of the variables. Then find the length of the sides. 2x7 y1 rhombus 2y5 x=5 y=4 3=3 3y9
Properties of Parallelograms Property: Both pairs of opposite sides are parallel. Theorem: Both pairs of opposite sides are congruent. Theorem: Both pairs of opposite angles are congruent. Theorem: The diagonals bisect each other. Property: Consecutive angles are supplementary.
Related Theorem: Theorem: If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.
Classifying Quadrilaterals Find the value of the variables. Then find the length of the sides. Find the measure of the angles. 7x1 (2a+30) 10 parallelogram 2x+4 (4a 4) x=3 10, 20, 20 a=17 64 6x+2
STAND DO YOU Do you understand? Mixed-up kid DKI STANDING A MISS Complete WS 6-1 and 6-2. Need an intermission? Solve these puzzles: STAND DO YOU Do you understand? Mixed-up kid DKI STANDING A MISS A misunderstanding
Need more work? Algebra Riddles for you Algebra Aces: Explain the rule for the following number arrangement: 8, 5, 4, 9, 1, 7, 6, 3, 2, 0 Alphabetical order! A man born in the year x2 died on his 87th birthday in the year (x+1)2. In what year was he born? 1849 Find all 2-digit positive integers for which the difference between the integer and the product of its digits is 12. 28 and 39.