sum of interior angles = 0 Rectangle
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1 im #27: What are the properties of parallellograms? o Now: The Family of Quadrilaterals Write the name of each quadrilateral and complete the properties. Geometry H Quadrilateral sum of interior angles = 0 Parallelogram both pairs of sides both pairs of equal both pairs of equal diagonals bisect 4 equal (is ) diagonals are diagonals bisect Rhombus Rectangle 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. 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)
2 2. Name oth pairs of sides are parallel. oth pairs of sides =. oth pairs of angles =. iagonals are equal. iagonals bisect each other. iagonals are perpendicular to each other. ll angles equal. iagonals bisect angles. onsecutive sides are equal. parallelogram rectangle rhombus square 3. 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. 4. 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
3 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 Q R (2) P = R (4) P + S = 180 P S f) Which statement is always true? (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? (1) (3) Δ ΔE T (2) ΔE ΔE (4) ΔE ΔE E 5. 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
4 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 sides are congruent. Given: Parallelogram Prove:,
5 3) If a quadrilateral is a parallelogram, then its angles are congruent. Given: Parallelogram Prove:, 4) If a quadrilateral is a parallelogram, then the diagonals bisect each other. Given: Parallelogram Prove: E E, E E E
6 Name Geometry H ate HW #27 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 Given parallelogram, m = (3x + 20) o and m = (2x + 30) o, find m. (2x + 30) o (3x + 20) o
7 6. Parallelogram. Find all possible measures of. x 2 5x x The vertices of parallelogram, STUV are S(-3,-2), T(4,-2), U(0,-5) and V(-7,-5). a) raw and label parallelogram STUV. b) Graph and give the coordinates of parallelogram S'T'U'V' as the image of the original after a translation: (x,y) (x + 1, y - 5) c) Graph and give the coordinates of parallelogram S"T"U"V" after a reflection of S'T'U'V' over the x-axis: r x-axis y x 8. Given: 1 2, E bisects Prove: E 2 E 1
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