P1 Math 2 Unit 1.5: Quadrilaterals: ay 5 Quadrilaterals Review Name t our next class meeting, we will take a quiz on quadrilaterals. It is important that you can differentiate between the definition of each of these quadrilaterals and various properties we have proven about them. Parallelogram o efinition: a quadrilateral with two pairs of opposite parallel sides (these will be given on the quiz!) iagonal creates two triangles iagonals bisect each other Opposite sides are Opposite angles are onsecutive angles are supplementary o Ways to prove a quadrilateral is a parallelogram: Use the definition (show it has two pairs of opposite parallel sides) If a quadrilateral has two pairs of opposite sides, then it is a parallelogram If a quadrilateral has two pairs of opposite angles, then it is a parallelogram If a quadrilateral has one pair of opposite sides that are both and parallel, then it is a parallelogram (You will prove this in #1 on this review) Rectangle: o efinition: a parallelogram (2 pairs of opposite parallel sides) with 4 right angles ll properties of parallelograms apply iagonals are o Ways to prove a quadrilateral is a rectangle: Use definition (show it is a parallelogram with 4 right angles) If a parallelogram has at least 1 right angle, then it is a rectangle If the diagonals of a parallelogram are, then it is a rectangle Rhombus: o efinition: a parallelogram (2 pairs of opposite parallel sides) with 4 sides ll properties of parallelograms apply iagonals are perpendicular o Ways to prove a quadrilateral is a rhombus: Use definition (show it is a parallelogram with 4 sides) If the diagonals of a parallelogram are perpendicular, then it is a rhombus Square: o efinition: a rectangle (2 opposite sides parallel and 4 right angles) with 4 sides ll properties of parallelograms apply o Ways to prove a quadrilateral is a square: Use definition (show it is a rectangle with 4 sides) à i.e., If a quadrilateral is both a rhombus and a rectangle, then it is a square
Trapezoid: o efinition: a quadrilateral with exactly one pair of parallel sides o How to prove a quadrilateral is a trapezoid: Use the definition (show there is exactly one pair of parallel sides) Isosceles trapezoid: o efinition: a quadrilateral with exactly one pair of parallel sides & with the other two sides to each other o Properties of isosceles trapezoids: iagonals are ase angles are (remember there are 2 pairs of base angles) o How to prove a quadrilateral is an isosceles trapezoid: Use the definition (show there is exactly one pair of parallel sides and that the other two sides are ) Kite: o efinition: a quadrilateral with two pairs of adjacent, sides One of the diagonals bisects a pair of opposite angles One diagonal is the perpendicular bisector of the other One pair of opposite angles are o How to prove a quadrilateral is a kite: Use the definition (prove there are two pairs of adjacent sides)
Relating Quadrilaterals Make a flowchart that illustrates the relationships between all of the following sets: quadrilaterals, parallelograms, rhombuses, rectangles, squares, kites, trapezoids, isosceles trapezoids
efinitions & Properties: Fill in the following chart of properties for the special quadrilaterals. Place a check mark in any box if the property holds true for the special quadrilateral listed. Place a star in the box if that description is part of the definition of that quadrilateral. Opposite sides parallel Opposite sides Opposite angles ll angles ll sides Only one pair of opposite sides parallel iagonals bisect each other iagonals iagonals perpendicular iagonals bisect opposite angles ase angles Only one diagonal bisects the other Only one pair of opposite angles are Parallelogram Rectangle Rhombus Square Isosceles Trapezoid Kite
Review Problems: omplete on a separate sheet of paper. 1. From pg. 520 (#31): F E 2. Given: F is a p- gram F E Prove: FE is a p- gram 3. Given: R is isosceles with base R K K Prove: RK is a p- gram R K 4. Given: NRTW is a p- gram NX TS WV PR X W V T Prove: XPSV is a p- gram S N P R
5. Given: is a p- gram bisects and Prove: is a rhombus 6. Given: GJMO is a p- gram OH GK MK is an altitude of MKJ Prove: OHKM is a rectangle O M G H J K 7. Given: is rectangle E F E F Prove: EF is an isosceles trapezoid I 8. Given: I bisects R I IR K R Prove: IR is a kite