University:
Missouri State University
Course:
MTH 460 | College Geometry
Academic year:

2022
Views:

174

Pages:

4
Author:

smammarejv5

Name: _____________________________________ Date: _____________ 6.5 – Special Parallelograms Three Special Types of Parallelograms: Rhombus Rectangle Square * Since these are also parallelograms, they have all the properties of parallelograms in addition to some other unique properties. * Theorems about Special Parallelograms: Rhombus: ▪ A quadrilateral is a rhombus if and only if… ▪ A parallelogram is a rhombus if and only if… ▪ A parallelogram is a rhombus if and only if… Rectangle: ▪ A quadrilateral is a rectangle if and only if… ▪ A parallelogram is a rectangle if and only if… What do the words “if and only if” imply in each of these definitions? Each figure below is a parallelogram. Identify the special type, by its most specific name, and explain your reasoning. 1) 2) 3) 4) Use the figure to find the missing measures. Given: DOGS is a rhombus. 𝒎∠DOG = 80o, GS = 4. 1) m∠OSD 2) DO 3) m∠ODS 4) m∠SXG 5) m∠ODX Find the value of x and y for the figure. 1) ABCD is a rectangle 2) ABCD is a square 3) ABCD is a rhombus AC = x2, BD = x + 72 m∠A = 4x + 4y m∠A = 15y - 35 m∠D = 8x – 4y m∠C = 20x, m∠D = 80 MATH is a parallelogram with diagonals intersecting at point O. Identify the special type based on the given conditions. ̅̅̅̅ ̅̅̅̅̅ ⊥ 𝐴𝐻 1) 𝑀𝑇 ̅̅̅̅̅ ⊥ 𝐴𝑇 ̅̅̅̅, 𝐴𝑀 ̅̅̅̅̅ ≅ 𝑀𝐻 ̅̅̅̅̅ 2) 𝑀𝐴 ̅̅̅̅ ̅̅̅̅̅ ≅ 𝐴𝐻 3) 𝑀𝑇 4) ∆𝐴𝑂𝑇 ≅ ∆𝑇𝑂𝐻 Complete the chart to compare the properties of all parallelograms. Property Parallelogram Rectangle Rhombus All angles are right angles Both pairs of opposite sides are parallel All sides are congruent Both pairs of opposite angles are congruent Diagonals bisect interior angles Diagonals are perpendicular Diagonals are congruent Diagonals bisect each other Both pairs of opposite sides are congruent Decide whether the statement is true or false and write the word on the line. __________ 1) All rhombuses are squares. __________ 2) A square has congruent diagonals. __________ 3) The diagonals of a rectangle sometimes bisect one another. __________ 4) Every rhombus is a parallelogram. The vertices of a quadrilateral are G = (1, 3), E = (3, 5), O = (7, 1) & M = (5, -1). Practice for your core: What type of quadrilateral is GEOM? Use coordinate geometry to determine your answer. Be sure to explain your reasoning. Square Complete the following proof. Given: HANK is a rhombus, ̅̅̅̅ 𝐻𝐸 ≅ ̅̅̅̅ 𝐹𝑁 Prove: EAFK is a parallelogram Statement Reason