Geometry Chapter 10

Question 1

A circle may be inscribed in

Answer 1

any regular polygon

Question 1

For a regular polygon of n sides: Each exterior angle e measures

Answer 1

360/n

Question 2

In a circle of radius r, the length l of an arch of measure n degrees equals

Answer 2

n/360 of the circumference of the circle

l=n/360 X2piR

pinR/180

Question 3

Area of a circle

Answer 3

1/2 Circumference(radius)

1/2 (2 pi radius)(radius)

pi r^2

Question 4

The length of an altitude of an equalateral triangle equals

Answer 4

the sum of the apothem and the radius

Question 5

Corresponding segments of regular polygons having the same number of sides are

Answer 5

in proportion.

(includes sides, perimeters, radii or circumferences of circumscribed or inscribed circles and such)

Question 5

Sector of a circle

Answer 5

part of a circle bounded by two radii and their intercepted arc.

Question 6

The area of a regular polygon equals

Answer 6

1/2 (perimeter)(apothem)

1/2(numberofsides)(lengthofsides)(apothem)

Question 8

If a regular polygon of n sides has a length of s

Answer 8

The perimeter is p=ns

Question 9

apothem of a regular hexagon equals

Answer 9

1/2 the radius X square root of 3

Question 9

If a regular polygon is inscribed in a circle, each segment cut off by the polygon has area equal to the difference between

Answer 9

the area of the circle and the area of the polygon divided by the number of sides.

Question 10

The apothem and radius of a square form a

Answer 10

45-45-90 triangle

Question 10

The apothem of a square equals

Answer 10

1/2 a side

or

1/2 the radius X square root 2

Question 10

Regular polygons having the same number of sides are

Answer 10

similar

Question 11

An equilateral polygon inscribed in a circle

Answer 11

is a regular polygon

Question 12

In an equilateral triangle, the apothem is

Answer 12

1/3 the altitude

Question 12

Circumference=

Answer 12

pi(diameter)

or

2(pi)(radius)

Question 14

For a regular polygon of n sides: Each interior angle i measures

Answer 14

(n-2)180/n

Question 14

The area of a minor segment of a circle equals

Answer 14

the area of its sector less the area of the triangle formed by its radii and chord

Question 16

The apothem and the radius of a hexagon form

Answer 16

30-60-90 Triangles

Question 17

In the regular hexagon, square, and equilateral triangle, what kind of figures are formed.

Answer 17

Special right triangles are formed when the apothem r and a radius R terminating in the same side are drawn.

Question 18

The length of a side in an equilateral Triangle equals

Answer 18

Radius X square root 3

Question 20

The apothem and radius of an equilateral triangle form

Answer 20

30-60-90 Triangles

Question 21

Radii of a regular polygon are

Answer 21

congruent

Question 22

Segment of a circle

Answer 22

part of a circle bounded by a chord and its arc. A minor segment of a circle is the smaller of the two segments thus formed.

Question 23

In an equilateral triangle, the Radius is

Answer 23

2/3 the altitude

Question 25

An apothem of a regular polygon

Answer 25

bisects the side to which it is drawn.

Question 26

A circle may be circumscribed about

Answer 26

any regular polygon

Question 28

For a regular polygon of n sides: Each central angle C measures

Answer 28

360/n

Question 29

The center of the circumscribed circle of a regular polygon is also

Answer 29

the center of its inscribed circle

Question 31

The length of a side of a regular hexagon equals

Answer 31

the length of the radius

Question 32

A radius of a regular polygon

Answer 32

bisects the angle to which it is drawn

Question 33

Area of a sector of n degree --------------------- Area of the Circle =

Answer 33

length of an arc of measure n degree --------------------- Circumference of the circle = n/360

Question 34

In a circle of radius r, the area K of a sector of measure n degree equals

Answer 34

n/360 of the area of the circle or K=n/360 X piR^2

Question 35

The side of a square equals

Answer 35

radius X square root 2

Question 36

In an equilateral triangle, the apothem equals

Answer 36

1/2 the Radius

Question 37

Areas of regular polygons having the same number of sides are to

Answer 37

each other as the squares of the lengths of any two corresponding segments

Question 38

Apothems of a regular polygon are

Answer 38

Congruent