Please click the speaker symbol on the left to hear the audio that accompanies some of the slides in this presentation. Quadrilaterals Quadrilateral: A Polygon with 4 sides and 4 angles. Sides: May or may not be congruent. Angles: The sum of all interior angles in a quadrilateral is 360o. Quad means “4” and lateral means “sides”. Types of Quadrilaterals In General …` Quadrilaterals are polygons that have 4 sides and 4 angles. Parallelograms A parallelogram has two parallel pairs of opposite sides. Parallelogram PropertiesSides Opposite sides are parallel Opposite sides are congruent Parallelogram PropertiesAngles Opposite angles are congruent Consecutive angles are supplementary m m Parallelogram PropertiesDiagonals Diagonals of a parallelogram meet at the midpoints. Divide the parallelogram into two congruent triangles Parallelogram- Area A = bh Area equals the base times the height. Theorems A quadrilateral is a parallelogram if any ONE of the following is true: Both pairs of opposite sides are || Both pairs of opposite sides are ≈ A pair of opposite sides is both || and ≈ Both pairs of opposite angles are ≈ Diagonals bisect each other Rectangles A rectangle has: two sets of opposite sides parallel, and four right angles. It is also a parallelogram, since it has two pairs of parallel sides. Rectangle Properties- Sides Opposite sides are parallel Opposite sides are congruent Rectangle Properties- Angles Four Right Angles Opposite angles are congruent Consecutive angles are supplementary m m Rectangle PropertiesDiagonals Diagonals of a rectangle are congruent. Diagonals bisect each other. Rectangle - Area A = bh Area equals the base times the height. Theorems If a parallelogram is a rectangle, then the diagonals are congruent. If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle. Rhombus … A rhombus is a parallelogram with four equal sides. It is not always a rectangle because a rhombus does not have to have 4 right angles. Rhombus Properties- Sides All four sides are congruent Rhombus Properties- Angles Same as all other parallelograms: Opposite angles are congruent Consecutive angles are supplementary Rhombus PropertiesDiagonals Diagonals of a rhombus are perpendicular. Each diagonal bisects the opposite angles. Rhombus- Area A = ½ d1 d2 Area equals ½ times the first diagonal times the second diagonal. Theorems If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. Squares … A square has: four right angles four congruent sides It is also a • rectangle • parallelogram • rhombus Square Properties Opposite sides are || All sides are ≈ Opposite angles are ≈ (90°) Consecutive angles are supplementary Diagonals are ≈ Diagonals bisect each other and angles Square - Area A = s2 Area equals the side times the side. Trapezoids … ` Trapezoids only have one pair of parallel sides. A Trapezoid is NOT a parallelogram. Parts of a Trapezoid The parallel sides are bases. The nonparallel sides are legs. Pairs of base angles share the same base. M and H are a pair of base angles. A and T are a pair of base angles. Isosceles Trapezoids Legs are ≈ Both pairs of base angles are ≈ Diagonals are ≈ Median of a Trapezoid Median is a segment that joins the midpoints of the legs. Parallel to the bases Length is ½ the sum of the bases median=½ (b1 + b2) Trapezoid - Area A = ½ h(b1 + b2) Area equals ½ the height times the sum of the bases. Quadrilaterals General Quadrilateral 4 sides, 4 angles Trapezoid Only 1 pair of parallel sides Quadrilaterals Parallelogram Opposite sides are parallel and congruent General Quadrilateral 4 sides, 4 angles Trapezoid Only 1 pair of parallel sides Quadrilaterals Parallelogram Opposite sides are parallel and congruent Rectangle A parallelogram with 4 right angles General Quadrilateral 4 sides, 4 angles Trapezoid Only 1 pair of parallel sides Quadrilaterals Parallelogram Opposite sides are parallel and congruent General Quadrilateral 4 sides, 4 angles Rectangle A parallelogram with 4 right angles Square A rectangle with 4 congruent sides Trapezoid Only 1 pair of parallel sides Quadrilaterals Parallelogram Opposite sides are parallel and congruent General Quadrilateral 4 sides, 4 angles Trapezoid Only 1 pair of parallel sides Rectangle A parallelogram with 4 right angles Rhombus A parallelogram with 4 congruent sides Square A rectangle with 4 congruent sides Comparison of Quadrilateral Properties Parallelogram Rectangle Square Rhombus Isosceles Trapezoid Opposite sides ≈ # of pairs # of pairs # of pairs # of pairs # of pairs Opposite sides || # of pairs # of pairs # of pairs # of pairs # of pairs Yes /No Yes /No Yes /No Yes /No Yes /No Diagonals Yes /No perpendicular Yes /No Yes /No Yes /No Yes /No Diagonals bisect each other Yes /No Yes /No Yes /No Yes /No Yes /No Diagonals bisect opposite angles Yes /No Yes /No Yes /No Yes /No Yes /No All angles 90° Yes /No Yes /No Yes /No Yes /No Yes /No Diagonals ≈ Comparison of Quadrilateral Properties Parallelogram Rectangle Square Rhombus Isosceles Trapezoid Opposite sides ≈ 2 pairs 2 pairs 2 pairs 2 pairs 1 pair Opposite sides || 2 pairs 2 pairs 2 pairs 2 pairs 1 pair Diagonals ≈ No Yes Yes No Yes Diagonals No perpendicular No Yes Yes No Diagonals bisect each other Yes Yes Yes Yes No Diagonals bisect opposite angles No No Yes Yes No All angles 90° No Yes Yes No No Venn Diagram of Quadrilaterals Parallelograms Rectangles Squares Rhombi Trapezoids