im #26: What are the properties of parallelograms? Geometry H o Now: omplete the following: Quadrilaterals Kite iagonals are perpendicular One pair of opposite angles is congruent Two distinct pairs of adjacent congruent sides (sum of interior angles = o ) Trapezoid a quadrilateral in which at least one pair of opposite sides is parallel Parallelogram both pairs of opposite sides both pairs of opposite equal both pairs of opposite equal diagonals bisect Isosceles Trapezoid Legs are congruent oth pairs of base angles are congruent iagonals are congruent Rhombus Rectangle 4 equal (is ) diagonals are diagonals bisect 4 equal (is ) diagonals are Square is and omplete: rhombus has all the properties of a. rectangle has all the properties of a. square has all the properties of a and a. n equiangular quadrilateral is a. n equilateral quadrilateral is a.
Exercises: 1. True or False? a) The sum of the angles of a rhombus is 360 o. b) Every rectangle is a parallelogram. c) Every square is a rhombus. d) Every rhombus is a square. e) Every rhombus is a parallelogram. f) The diagonals of a rectangle are equal. g) quadrilateral with four equal sides is a rhombus. h) The consecutive angles of a rhombus are equal. i) If a quadrilateral is equiangular, it is a rectangle. j) square is a rectangle and a rhombus. 2. etermine the most specific name of the quadrilateral based on the markings in the diagram. (iagram is not drawn to scale.) a) b) c) d) 3. QRST is a parallelogram. Find x, y, and z. T 5x Q 76 o 2y 5 57 o y+4 (3z) o S 27 R
Proving the properties of parallelograms: 1) If a quadrilateral is a parallelogram, a diagonal divides the parallelogram into two congruent triangles. Given: Parallelogram, diagonal Prove: Δ Δ 2) If a quadrilateral is a parallelogram, then its opposite sides are congruent. Given: Parallelogram, diagonal Prove:,
3) If a quadrilateral is a parallelogram, then its opposite angles are congruent. Given: Parallelogram, diagonal Prove:, 4) If a quadrilateral is a parallelogram, then the diagonals bisect each other. Given: Parallelogram, diagonal Prove: E E, E E
Name Geometry H ate HW #26 1. a. If the triangles are congruent, write the congruence statement: b. Which triangle congruence criterion guarantees (a)? c. TG corresponds with: 2. Name the quadrilateral as specifically as possible, based on the given characteristics. a) an equilateral quadrilateral b) an equiangular parallelogram c) a regular quadrilateral d) a parallellogram with perpendicular diagonals 3. lways, Sometimes, or Never true? a) The diagonals of a rhombus are perpendicular. b) If the diagonals of a parallelogram are equal, it is a square. c) djacent sides of a rhombus are unequal. d) onsecutive angles of a parallelogram are supplementary. 4. Given parallelogram with diagonals and, solve for x and y. 15 3x y 4x+2y 80 5. Parallelogram. Find all possible measures of. x 2 5x x + 40
6. Multiple hoice. a) If a quadrilateral has equal diagonals, it must be a (1) square (2) rhombus (3) rectangle (4) quadrilateral b) If the diagonals of a parallelogram are perpendicular and not equal, the parallelogram is (1) rectangle (2) square (3) rhombus (4) kite c) Two consecutive angles of a rhombus are (1) equal (2) complementary (3) linear (4) supplementary d) The diagonals of a rhombus (1) are equal (2) are perpendicular (3) are parallel (4) are adjacent e) Which statement is not true for every given parallelogram PQRS? (1) PQ = SR (3) PR SQ T (2) P = R (4) P + S = 180 f) Which statement is always true? P S (1) The diagonals of a parallelogram are congruent. (2) The diagonals of a parallelogram bisect the angles of the parallelogram. (3) The diagonals of a parallelogram bisect each other. (4) The diagonals of a parallelogram are perpendicular to each other. g) In parallelogram, diagonals and intersect at point E. Which statement is always true? T (1) (3) Δ ΔE (2) ΔE ΔE (4) ΔE ΔE Q E R Review: 1) Given: 1 2, E bisects Prove: E 1 2 E