Advanced Geometry Polygons Lesson 4 Other Quadrilaterals Rectangles

Advanced Geometry Polygons Lesson 4 Other Quadrilaterals

Rectangles four right angles Characteristics of Rectangles █ Diagonals are congruent. █ All characteristics of a parallelogram are still true.

Rhombus Plural: Rhombi four congruent sides Characteristics of Rhombi The diagonals are perpendicular. Each diagonal bisects a pair of opposite angles. All characteristics of parallelograms apply.

Squares both a rectangle and a rhombus Characteristics of Squares §All characteristics of a rectangle apply. §All characteristics of a rhombus apply. §All characteristics of a parallelogram apply.

Kites two distinct pairs of adjacent congruent sides

Trapezoids exactly one pair of parallel sides Parts of a Trapezoid bases – the parallel sides legs – the non-parallel sides base angles –a pair of angles that touch a base

Isosceles Trapezoid congruent legs Characteristics of Isosceles Trapezoids Ø Each pair of base angles is congruent. Ø The diagonals are congruent.

Median of a Trapezoid segment joins the midpoints of the legs 36 28 * The median is parallel to the bases. * The length of the median is half the sum of the bases.

Example: Quadrilateral RSTU is a rectangle. If RT = 6 x + 4 and SU = 7 x – 4, find x.

Example: Quadrilateral LMNP is a rectangle. If m∠MNL = 6 y + 2, m∠MLN = 5 x + 8, and m∠NLP = 3 x + 2, find x.

Example: Use rhombus LMNP and the given information to find the value of each variable. Find m∠PNL if m∠MLP = 64. Find y if m∠ 1 = y² - 54.

Example: DEFG is an isosceles trapezoid with median a) Find DG if EF = 20 and MN = 34. b) Find m∠ 1, m∠ 2, m∠ 3, & m∠ 4, if m∠ 1 = 3 x + 5 and m∠ 3 = 6 x – 5.

Example: Given each set of vertices, determine whether quadrilateral EFGH is a rhombus, a rectangle, or a square. List all that apply. Explain your reasoning.

Show that if LNPR is a rectangle and then. Given: Prove: Proof: Statements: Reasons: ,