other quadrilaterals
DESCRIPTION
Other Quadrilaterals. Advanced Geometry Polygons Lesson 4. 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. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Other Quadrilaterals](https://reader035.vdocuments.mx/reader035/viewer/2022062305/56814c24550346895db928c6/html5/thumbnails/1.jpg)
Other Quadrilaterals
Advanced GeometryPolygons Lesson 4
![Page 2: Other Quadrilaterals](https://reader035.vdocuments.mx/reader035/viewer/2022062305/56814c24550346895db928c6/html5/thumbnails/2.jpg)
Rectanglesfour right angles
Characteristics of Rectangles
█ Diagonals are congruent.
█ All characteristics of a parallelogram are still true.
![Page 3: Other Quadrilaterals](https://reader035.vdocuments.mx/reader035/viewer/2022062305/56814c24550346895db928c6/html5/thumbnails/3.jpg)
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.
![Page 4: Other Quadrilaterals](https://reader035.vdocuments.mx/reader035/viewer/2022062305/56814c24550346895db928c6/html5/thumbnails/4.jpg)
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.
![Page 5: Other Quadrilaterals](https://reader035.vdocuments.mx/reader035/viewer/2022062305/56814c24550346895db928c6/html5/thumbnails/5.jpg)
Kitestwo distinct pairs of adjacent congruent sides
![Page 6: Other Quadrilaterals](https://reader035.vdocuments.mx/reader035/viewer/2022062305/56814c24550346895db928c6/html5/thumbnails/6.jpg)
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
![Page 7: Other Quadrilaterals](https://reader035.vdocuments.mx/reader035/viewer/2022062305/56814c24550346895db928c6/html5/thumbnails/7.jpg)
congruent legs
Isosceles Trapezoid
Each pair of base angles is congruent.
The diagonals are congruent.
Characteristics of Isosceles Trapezoids
![Page 8: Other Quadrilaterals](https://reader035.vdocuments.mx/reader035/viewer/2022062305/56814c24550346895db928c6/html5/thumbnails/8.jpg)
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
![Page 9: Other Quadrilaterals](https://reader035.vdocuments.mx/reader035/viewer/2022062305/56814c24550346895db928c6/html5/thumbnails/9.jpg)
Example:Quadrilateral RSTU is a rectangle. If RT = 6x + 4 and SU = 7x – 4, find x.
![Page 10: Other Quadrilaterals](https://reader035.vdocuments.mx/reader035/viewer/2022062305/56814c24550346895db928c6/html5/thumbnails/10.jpg)
Example:Quadrilateral LMNP is a rectangle. If
m∠MNL = 6y + 2, m∠MLN = 5x + 8,
and m∠NLP = 3x + 2, find x.
![Page 11: Other Quadrilaterals](https://reader035.vdocuments.mx/reader035/viewer/2022062305/56814c24550346895db928c6/html5/thumbnails/11.jpg)
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.
![Page 12: Other Quadrilaterals](https://reader035.vdocuments.mx/reader035/viewer/2022062305/56814c24550346895db928c6/html5/thumbnails/12.jpg)
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.
![Page 13: Other Quadrilaterals](https://reader035.vdocuments.mx/reader035/viewer/2022062305/56814c24550346895db928c6/html5/thumbnails/13.jpg)
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
![Page 14: Other Quadrilaterals](https://reader035.vdocuments.mx/reader035/viewer/2022062305/56814c24550346895db928c6/html5/thumbnails/14.jpg)
Show that if LNPR is a rectangle and ,then .
LM PQMR NQ
Given:
Prove:Proof:
Statements: Reasons: