Other Quadrilaterals Advanced Geometry Polygons Lesson 4.

Other Quadrilaterals

Advanced GeometryPolygons Lesson 4

Rectanglesfour right angles

Characteristics of Rectangles

█ Diagonals are congruent.

█ All characteristics of a parallelogram are still true.

Rhombusfour congruent sides

Characteristics of Rhombi The diagonals are perpendicular.

Plural: Rhombi

All characteristics of parallelograms apply.

Each diagonal bisects a pair of opposite angles.

All characteristics of a parallelogram apply.

Squaresboth a rectangle and a rhombus

Characteristics of Squares

All characteristics of a rectangle apply.

All characteristics of a rhombus apply.

Kitestwo distinct pairs of adjacent congruent sides

exactly one pair of parallel sides

base angles –

Trapezoids

Parts of a Trapezoidbases –

legs – AB and DC

AD and BC

A and B D and C

the parallel sides

the non-parallel sides

a pair of angles that touch a base

congruent legs

Isosceles Trapezoid

Each pair of base angles is congruent.

The diagonals are congruent.

Characteristics of Isosceles Trapezoids

joins the midpoints of the legs

* The median is parallel to the bases.

Median of a Trapezoid

* The length of the median is half the sum of the bases.

36

28

segment

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

Example:Quadrilateral LMNP is a rectangle. If

m∠MNL = 6y + 2, m∠MLN = 5x + 8,

and m∠NLP = 3x + 2, find x.

Example: Use rhombus LMNP and the given information to find the value of each variable.

Find y if m∠1 = y² - 54.

Find m∠PNL if m∠MLP = 64.

MN

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 = 3x + 5 and m∠3 = 6x – 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.

1,5 , (6,5), (6,10), 1,10E F G H

Show that if LNPR is a rectangle and ,then .

LM PQMR NQ

Given:

Prove:Proof:

Statements: Reasons: