Theorems
Measure of an EXTERIOR angle of a regular n-gon
360/n?
The SUM of the INTERIOR angle measures of a TRIANGLE is_________
(n-2)180
(3-2)180
1(180)
180?
If a quadrilateral is a parallelogram, then ______.
(Name any of the 4 properties of a parallelogram)
*answers may vary*
its opposite sides are congruent?
its consecutive angles are supplementary?
its opposite angles are congruent?
its diagonals bisect each other?
A _____ polygon is a polygon with all sides congruent.
Equilateral?
Find the sum of the angle measures of a 60-gon
(n-2)180
(60-2)180
58(180)
10,440?
The measure of EACH interior angle of a regular n-gon
(n-2)180/n?
The measure of an EXTERIOR angle of a regular 16-gon is ______
(Round to the nearest tenth)
360/n
360/16
22.5?
*see picture*
Find the value of x in the parallelogram
180-80
x=100 degrees?
A polygon that is both equilateral and equiangular
Regular Polygon?
Find the measure of one angle in a regular 36-gon. Round to the nearest tenth
(n-2)180/n
(36-2)180/36
34(180)/36
6120/36
170?
The sum of the measures of the interior angles of an n-gon is (n-2)180
Polygon Angle-Sum Theorem?
If a quadrilateral is a _______, then its opposite sides are congruent
parallelogram?
*see picture*
Find the missing lengths of the parallelogram
6y+1=4y+9 2x-5=x+7
6y=4y+8 x-5=7
2y=8
x=12? y=4?
Segment AE and ED =25?
Segment CE and EB=19?
Angles of a polygon that share a side
Consecutive angles?
*see picture*
Find the values of x and y, then find QT, TS, PT,TR
x+2=y 2x=y+3
(use substitution)
2x=(x+2)+3 x+2=y
2x=x+5 (5)+2=y
x=5? y=7?
*See Picture*
Find the missing angle measures
124+118+100+100+x=(n-2)180
442+x=(5-2)180
442+x=3(180)
442+x=540
x=98 degrees?
If a ______ is a parallelogram, then its opposite ____ are congruent.
quadrilateral?
angles?
Use the picture on the board
Find each value
(m<a, m<D, x, and AB)
m<a= 53 degrees?
m<d= 127 degrees?
x=5?
AB=7?
Parallelogram
a quadrilateral with both pairs of opposite sides parallel?
*see picture*
If line AE is parallel to line BF, CG, and DH and EF=FG=GH=6 and AD=15, find EH and CD.
EF=FG=GH=6
EF+FG+GH=6+6+6=12
EH=12?
CD=AD/3
CD=(15)/3=5 CD=5?
*See Picture*
Find the values of the variables for each REGULAR polygon
360/n 180-120=60
360/3
x=120 degrees? y=60 degrees?
*see picture*
If lines AB,CD,and EF are parallel and line AC is congruent to line CE then line ___ is congruent to line ____.
BD?
DF?
In the figure, Line AE is parallel to line BF, CG, and DH
AB=BC=CD=2 and EF=2.25. Find EH
EF=FG=GH (Theorem 6-7)
EH=EF+FG+GH (Segment Addition Postulate)
EH=2.25+2.25+2.25=6.75?
Polygon Angle-Sum Theorem
*You can't only say the formula, you must state it in a complete sentence
The sum of the measures of the interior angles of an n-gon is (n-2)180?
The measure of the EXTERIOR angle of a REGULAR polygon is 14.4. Find the measure of an INTERIOR angle and the number of sides.
180-14.4=165.6
Interior angle=165.6?
(n-2)180/n=165.6
(n-2)180=165.6n
180n-360=165.6n
14.4n=360
n=25?