Polygon formulas

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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