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:
Top Related