Transcript Other Quadrilaterals - Petal School District

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
AB and DC
legs – the non-parallel sides
AD and BC
base angles –a pair of angles that touch a base
A and B
D and C
Isosceles Trapezoid
congruent legs
Characteristics of Isosceles Trapezoids
 Each pair of base angles is congruent.
 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 = 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 m∠PNL if m∠MLP = 64.
Find y if m∠1 = y² - 54.
Example:
DEFG is an isosceles trapezoid with median MN
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.
E 1,5 , F (6,5), G(6,10), H 1,10 
Show that if LNPR is a rectangle and LM  PQ,
then MR  NQ.
Given:
Prove:
Proof:
Statements:
Reasons: