Construction of Quadrilaterals

8/9/2019 Construction of Quadrilaterals

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$roperties of &ho'*us: Sides X"iagonals X ngles &elated: rea of &ho'*us

#iagonals of a -hombus

iagonalsare perpendicular $

" 0 '(

" : 0 '(

: 0 '(

0 '(

s the four;sided shape *elow, 0-


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!nngles of a -hombusThe diagonals *isect the vertex angles of a rhombus.

proof of this propert+ of the diagonals
http://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rhombus.php#sidesRhombushttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rhombus.php#sidesRhombushttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rhombus.php#diagonalRhombushttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rhombus.php#diagonalRhombushttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rhombus.php#angelRhombushttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rhombus.php#angelRhombushttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rhombus.php#areaRhombushttp://www.mathwarehouse.com/dictionary/B-words/definition-of-bisect.phphttp://www.mathwarehouse.com/geometry/congruent_triangles/congruent-parts-CPCTC.php#diagonalRhombushttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rhombus.php#sidesRhombushttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rhombus.php#diagonalRhombushttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rhombus.php#angelRhombushttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rhombus.php#areaRhombushttp://www.mathwarehouse.com/dictionary/B-words/definition-of-bisect.phphttp://www.mathwarehouse.com/geometry/congruent_triangles/congruent-parts-CPCTC.php#diagonalRhombus


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What is the measure of the following angles in rhombus !" #P! #

!"#

"ns#er

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! generaliHation about the angles of a rhombus7ou can think of a rhombus as four triangles that are created by the diagonals

such as . What is true about the outside angles in each triangleP

!n examples of outside angles are

"ns#er
http://www.transtutors.com/submit-assignment.aspx?ref=mathwarehttp://www.mathwarehouse.com/geometry/triangles/http://www.mathwarehouse.com/geometry/angle/http://www.transtutors.com/submit-assignment.aspx?ref=mathwarehttp://www.mathwarehouse.com/geometry/triangles/http://www.mathwarehouse.com/geometry/angle/


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What is the value of x if angle " ! $ 'x B) and angle ! # $ 4) Q xP

"ns#er

What is the value of x, given the angle measurements belowP

"ns#er


!rea of -hombus
http://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rhombus.php#sidesRhombushttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rhombus.php#sidesRhombushttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rhombus.php#diagonalRhombushttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rhombus.php#diagonalRhombushttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rhombus.php#angelRhombushttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rhombus.php#angelRhombushttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rhombus.php#areaRhombushttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rhombus.php#sidesRhombushttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rhombus.php#diagonalRhombushttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rhombus.php#angelRhombushttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rhombus.php#areaRhombus


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The formula for area of A Rhombus

"rea 0 J/diagonal 1 = diagonal 2)

What is the area of FI0DP

"ns#er

$utting t ll Together


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T!- is a rhombus. The measure of diagonals ! is )% and the measureof T- is 42, what is the perimeter of this rhombusP

Rectangle: Shape and Properties
http://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rhombus.php#diagonalRhombushttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rhombus.php#diagonalRhombus


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! special kind of parallelogram

This $age: "iagonal &elated: $roperties of parallelogra's X s a s#uare a rectangle= Xs#uare

rectangle is a parallelogra' with 4 right angles. -ow, since arectangle is a parallelogra' , its opposite sides 'ust *e congruent and it'ust satisf+ all other properties of parallelogra's .

The 8roperties of a -ectangle8 %ig't Angles

&n a rectangle all angles are'(
http://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rectangle.php#diagnoalRectanglehttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/http://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/is_square_rectangle.phphttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/is_square_rectangle.phphttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/square.phphttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelogramshttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelogramshttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelogramshttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rectangle.php#diagnoalRectanglehttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/http://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/is_square_rectangle.phphttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/square.phphttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelogramshttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelogramshttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms


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Diagonals of %ectangle

T e diagonals of arectangleare con ruent $

It s easy to prove that the diagonals of a rectangle with the 8ythagoreantheorem. Clic here to see the proof .

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Practice Problems

This $age: "iagonal &elated: $roperties of parallelogra's X s a s#uare a rectangle= Xs#uare

8roblem 4/In rectangle T!- below, ! $1, what is the length of -TP
http://www.mathwarehouse.com/dictionary/C-words/congruent.htmlhttp://void%280%29/http://www.transtutors.com/submit-assignment.aspx?ref=mathwarehttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rectangle.php#diagnoalRectanglehttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/http://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/is_square_rectangle.phphttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/is_square_rectangle.phphttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/square.phphttp://www.mathwarehouse.com/dictionary/C-words/congruent.htmlhttp://void%280%29/http://www.transtutors.com/submit-assignment.aspx?ref=mathwarehttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rectangle.php#diagnoalRectanglehttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/http://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/is_square_rectangle.phphttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/square.php


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"ns#er

8roblem )/

If side 5> $ 4) and side 5E $ 1, what is the length of the other two sidesP

"ns#er

8roblem '/

Fow Eong is 5= and 5 in the rectangle

pictured on the leftP


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"ns#er

Challenge $ro*le' What is the value of x in rectangle T!- belowP

"ns#er

Square:

A rhombus and a rectangleA square is rhombus as !ell as a rectan le " Therefore# asquare is a shape !ith four con ruent sides$the rhombus components% and four &0' an les$the rectan le component%"

links

! square has the properties of a rhombus and a rectangle. Its sides intersect atK23 and all four sides are congruent.
http://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rhombus.phphttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rectangle.phphttp://www.mathwarehouse.com/dictionary/C-words/congruent.htmlhttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rhombus.phphttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rectangle.phphttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rhombus.phphttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rectangle.phphttp://www.mathwarehouse.com/dictionary/C-words/congruent.htmlhttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rhombus.phphttp://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rectangle.php


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;xample of square:

Congruent or Congruence

#efinition: congruent means that ob


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!rea $ Y diagonal 4/ diagonal ) /

Isosceles Trapezoid

An trapezoid with congruent Legs

!ase ngles X "iagonals

The defining trait of this special type of trapeHoid is that the two nonBparallelsides 6W and 7 below/

are congruent .

"ase !ngles

The base angles of an isosceles trapeHoid are congruent.

If you know that angle "!# is %% 3, what is the measure of !# P

!nswer
http://www.mathwarehouse.com/geometry/quadrilaterals/isosceles-trapezoid.php#baseAnglehttp://www.mathwarehouse.com/geometry/quadrilaterals/isosceles-trapezoid.php#diagonalsIsosceleshttp://www.mathwarehouse.com/dictionary/C-words/congruent.htmlhttp://www.mathwarehouse.com/geometry/quadrilaterals/isosceles-trapezoid.php#baseAnglehttp://www.mathwarehouse.com/geometry/quadrilaterals/isosceles-trapezoid.php#diagonalsIsosceleshttp://www.mathwarehouse.com/dictionary/C-words/congruent.html


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!" $ 4'2, what other angle measures 4'2 degreesP

!nswer

What is the value of < in the isoscles trapeHoid belowP!nswer

!ase ngles X "iagonals

#iagonals of Isosceles TrapeHoid

The diagonals of an isoscels trapeHoid are congruent. What is the value of x
http://www.mathwarehouse.com/geometry/quadrilaterals/isosceles-trapezoid.php#baseAnglehttp://www.mathwarehouse.com/geometry/quadrilaterals/isosceles-trapezoid.php#diagonalsIsosceleshttp://www.mathwarehouse.com/geometry/quadrilaterals/isosceles-trapezoid.php#baseAnglehttp://www.mathwarehouse.com/geometry/quadrilaterals/isosceles-trapezoid.php#diagonalsIsosceles


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belowP use your knowledge about diagonals R/!nswer

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http://www.mathwarehouse.com/geometry/quadrilaterals/isosceles-trapezoid.php#diagonalsIsosceleshttp://www.mathwarehouse.com/geometry/http://www.mathwarehouse.com/geometry/quadrilaterals/isosceles-trapezoid.php#diagonalsIsosceleshttp://www.mathwarehouse.com/geometry/


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! plane has 2 "i'ensions and is often called 2" /:

$oint, >ine, $lane andSolid

! point has no dimensions,

only location

! line is oneBdimensional

plane is two di'ensional

! solid is threeBdimensional

$lane s $lain

In geometry a ZplaneZ is a flat surface with no thickness.

"ut a ZplainZ is a treeless 'ostl+ flat e)panse of land ... it is also flat, butnot in the pure sense we use in geometry.

"oth words have other meanings too: 8lane can mean an airplane, a level, ora tool for cutting things flatO 8lain can mean without special things, or wellunderstood.

'agine

Imagine you lived in a twoBdimensional world. 7ou could travel around, visitfriends, but nothing in your world would have height.

7ou could measure distances and angles.
http://www.mathsisfun.com/geometry/point.htmlhttp://www.mathsisfun.com/geometry/line.htmlhttp://www.mathsisfun.com/geometry/solid-geometry.htmlhttp://www.mathsisfun.com/geometry/point.htmlhttp://www.mathsisfun.com/geometry/line.htmlhttp://www.mathsisfun.com/geometry/solid-geometry.html


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7ou could travel fast or slow. 7ou could go forward, backwards or sideways.7ou could move in straight lines, circles, or anything so long as you never goup or down.

What would life be like living on a planeP

Co''on S+'*ols ?sed in @eo'etr+

ymbols save time and space when writing. Fere are the most commongeometrical symbols:

()mbol *eanin +xample ,n ords

Triangle": as 3

equal sidesTriangle ABC has three equal

sides

"ngle ": is 45The angle formed by ABC is

45 degrees.

Perpendicular ": The line AB is perpendicular to line CD

Parallel MN E,The line E is parallel to line

!"

egrees3+( ma es a

full circle

Rig t "ngle /'( ) is '( A right angle is #$ degrees

Aine Segment O":O ": The line bet%een A and B

Aine O":OThe in&nite line that includes

A and B

Ray O":OThe line that starts at A' goesthrough B and continues on
http://www.mathsisfun.com/triangle.htmlhttp://www.mathsisfun.com/angles.htmlhttp://www.mathsisfun.com/perpendicular-parallel.htmlhttp://www.mathsisfun.com/perpendicular-parallel.htmlhttp://www.mathsisfun.com/geometry/degrees.htmlhttp://www.mathsisfun.com/rightangle.htmlhttp://www.mathsisfun.com/triangle.htmlhttp://www.mathsisfun.com/angles.htmlhttp://www.mathsisfun.com/perpendicular-parallel.htmlhttp://www.mathsisfun.com/perpendicular-parallel.htmlhttp://www.mathsisfun.com/geometry/degrees.htmlhttp://www.mathsisfun.com/rightangle.html


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ongruent /sames ape and size)

": MN

Triangle ABC is congruent totriangle DE

Similar /same s apedi-erent size) MN ?I

Triangle DE is similar totriangle ()*

T erefore a=b b=aa equals b' therefore b equals

a

A)a'ple:

When someone writes: In !" , "! is

They are really saying: ZIn triangle !" , the angle "! is a right angleZ

-a'ing ngles

*or angles the central letter is where the angle is.

A)a'ple:

when you see Z !" is %13Z, then the point Z"Z is wherethe angle is.
http://www.mathsisfun.com/geometry/congruent.htmlhttp://www.mathsisfun.com/geometry/similar.htmlhttp://www.mathsisfun.com/geometry/congruent.htmlhttp://www.mathsisfun.com/geometry/similar.html


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5athematical ymbols

ymbols save time and space when writing. Fere are the 'ost

co''on mathematical symbols:

()mbol *eanin +xample

< add 3 0 1(

* su!tract 5*2 0 3

= multiply 4=3 0 12

L di%ide 2(L5 0 4

/ ) grouping sym!ols 2/a*3)

Q grouping sym!ols 2 a*3/!


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T erefore a=b b=a


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ymbols in !lgebra

Co''on S+'*ols ?sed in lge*ra

ymbols save time and space when writing. Fere are the most commonalgebraic symbols:

()mbol *eanin +xample

< add 3 0 1(

* su!tract 5*2 0 3

= multiply 4=3 0 12

multiply /so O=O does not loo li eO8O)

4[3 0 12

L di%ide 2(L5 0 4

square root /OradicalO) Z4 0 2

cu!e root

n t root

/ ) grouping sym!ols /round!rac ets)

2/a*3)

Q grouping sym!ols /square!rac ets)

2 a*3/!


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appro8imately equal to . 3$14

V not equal to . V 2

W X less t an less t an or equal to 2 W 3

; Y greater t an greater t an orequal to

5 ; 1

implies /if $$$ t en) a and ! are odd a

Oif and only if O or i/ or Oisequi%alent toO

80y


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Measuring angles with a protractor - lesson &video

This 4th grade geometry lesson explains angle measure, how to measure angleswith a protractor, and has varied exercises for the students.

Remember how one side of the angle traces out a circular arc? We usethat circle to measure how big the angle is. We loo at how much the angle has!opened" as compared to the full circle.

#ngles are measured in degrees . The symbol for degrees is a little circle $.

The %&'' ()R('* is + -$ + - degrees/.

# half circle or a straight angle is 01-$.

# 2uarter circle or a right angle is 3-$.

how the angles below using two pencils. Try to !see" the circle that is traced outin the air.


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This is a 1-degree angle!

an obtuse angle5 067$ a right angle5 3-$

8ow to measure an angle with a protractor 9

:lace the midpoint of the protractor on the ;*RT*< of the angle.

'ine up one side of the angle with the =ero line of the protractor where yousee the number -/.

Read the degrees where the other side crosses the number scale.

Ta e care to read from the right set of numbers. # protractor has two sets ofnumbers9 one set goes from - to 01-, the other set from 01- to -. Which one you


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read depends on how you place the protractor9 place it so that one side of theangle lines up with one of the =eros, and read that set of numbers.

)n the examples above we lined up the one side of the angle with the =ero of thelower set of numbers, so we need to read the lower set of numbers.

0. >easure the angles.

a. $ b. $

c. $

d. $

6. >easure the angles. 'abel each angle as acute or obtuse.


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a. $

b. $

c. $

d. $

e. $

f. $


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+. Tasha measured an acute angle, and got 04 $. The teacher pointed outthat she had read the wrong set of numbers on the protractor.What is the correct angle measure for the angle she measured?

4. >easure the following angles using your own protractor. )f you need to, ma e thesides of the angles

longer with a ruler.


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. @raw four dots, and connect them so that you get a 2uadrilateral.>easure all the angles of your 2uadrilateral. Then add the angle measures.@id you get + - degrees, or close?


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http://www.rockingham.k12.va.us/resources/elementary/5math.htmhttp://www.mathwarehouse.com/geometry/quadrilaterals/http://www.mathplayground.com/measuringangles.htmlhttp://www.rockingham.k12.va.us/resources/elementary/5math.htmhttp://www.mathwarehouse.com/geometry/quadrilaterals/http://www.mathplayground.com/measuringangles.html

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