Polygon formulas
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Transcript of Polygon formulas
Polygon formulas
Quad Properti
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Distance/ midpoint
Polygon formulas (backwards
)
Bisect/Midpoint
story problems
Potporri
Find the sum of the interior angles of an
octagon
Back
1080˚
Back
Find the measure of 1 interior angle of a regular
pentagon
108 ˚
Back
Find the sum of the exterior angles of a
dodecagon
360 ˚
Back
Find the measure of 1 exterior angle of a
regular 20-gon
18˚
Back
Find the sum of the interior angles of a
septagon
900 ˚
Congruent diagonals
Back
R, S, IT
Which quadrilaterals have:
(P = parallelogram, R = rectangle, Rh = rhombus, S = square, IT = isosceles trapezoid)
Back
4 congruent sides
Rh, S
Which quadrilaterals have:
(P = parallelogram, R = rectangle, Rh = rhombus, S = square, IT = isosceles trapezoid)
Back
Opp angles congruent
P, R, Rh, S
Which quadrilaterals have:
(P = parallelogram, R = rectangle, Rh = rhombus, S = square, IT = isosceles trapezoid)
Back
Perpendicular diagonals
Rh, S
Which quadrilaterals have:
(P = parallelogram, R = rectangle, Rh = rhombus, S = square, IT = isosceles trapezoid)
Back
Diagonals that bisect angles
Rh, S
Which quadrilaterals have:
(P = parallelogram, R = rectangle, Rh = rhombus, S = square, IT = isosceles trapezoid)
(3, 4) (-2, 5)
Back
D = 5.10
M (½ , 4 ½)
Find the distance AND the midpoint:
Back
(7, 0) (-1, 6)
Find the distance AND the midpoint:
D = 10
M (3 , 3)
Back
(-7, 5) (2, 8)
Find the distance AND the midpoint:
D = 9.49
M (-2 ½, 6 ½)
Back
(-12, 5) (-3, 9)
Find the distance AND the midpoint:
D = 9.85
M (-7 ½, 7 )
Back
(0, 16) (-7, -8)
Find the distance AND the midpoint:
D = 25
M (-3 ½, 4)
E = 40˚. Name the polygon.
Back
360 = 9 Regular nonagon 40
I = 150˚. Name the polygon
Back
180 – 150 = 30 Regular Dodecagon
360 = 12 30
Si = 720˚. Name the polygon.
Back
720 = 180(n – 2) hexagon 4 = n – 2 6 = n
I = 108˚. Name the polygon.
Back
180 – 108 = 72 Regular pentagon
360 = 5 72
Si = 1620˚. Name the polygon.
Back
1620 = 180(n – 2) 11-gon 9 = n – 2 11 = n
Ray BD bisects <ABC. m<ABD = 6xm<CBD = 4x + 14Find m<ABC.
Back
84 ˚
6x = 4x + 14 <ABC = 2(6x)2x = 14 = 12(7) x = 7
O is the midpoint of HT.OH = 3x + 1TH = 7x – 6 Find HT.
Back
50
2(3x + 1) = 7x – 6 HT = 7(8) – 6 6x + 2 = 7x – 6 8 = x
Ray OD bisects <COL<LOD = 2x + 6<COL = 6x – 8 Find m <DOC.
Back
26 ˚
2(2x + 6) = 6x – 8 <DOC = 2x + 64x + 12 = 6x – 8 = 2(10) + 6 20 = 2x 10 = x
A is between C and T. CA = 2x + 1AT = 4x – 1 Find CT
Back
12
2x + 1 = 4x – 1 CT = 2(2x + 1) 2 = 2x 1 = x
Ray ID bisects <BIR<BID = 5x + 5<RID = 3x + 23Find m <DIR
Back
50 ˚
5x + 5 = 3x + 23 <DIR = 3x + 232x = 18 3(9) + 23 x = 9
Find the measure of 1 interior angle of a regular 25-gon.
Back
180(25 – 2) 25
165.6 ˚
Name all the quadrilaterals with:
4 right angles
Back
R, S
Find the distance between (-5, 9) and (0, -3)
Back
13
The measure of 1 exterior angle of a regular polygon is 45 ˚. Find the number of sides.
Back
360 45
8
E = 40˚Name the polygon
Back
360 40
Regular nonagon