Geometry Chapter 10 Flashcards
A circle may be inscribed in
any regular polygon
For a regular polygon of n sides: Each exterior angle e measures
360/n
In a circle of radius r, the length l of an arch of measure n degrees equals
n/360 of the circumference of the circle
l=n/360 X2piR
pinR/180
Area of a circle
1/2 Circumference(radius)
1/2 (2 pi radius)(radius)
pi r^2
The length of an altitude of an equalateral triangle equals
the sum of the apothem and the radius
Corresponding segments of regular polygons having the same number of sides are
in proportion.
(includes sides, perimeters, radii or circumferences of circumscribed or inscribed circles and such)
Sector of a circle
part of a circle bounded by two radii and their intercepted arc.
The area of a regular polygon equals
1/2 (perimeter)(apothem)
1/2(numberofsides)(lengthofsides)(apothem)
If a regular polygon of n sides has a length of s
The perimeter is p=ns
apothem of a regular hexagon equals
1/2 the radius X square root of 3
If a regular polygon is inscribed in a circle, each segment cut off by the polygon has area equal to the difference between
the area of the circle and the area of the polygon divided by the number of sides.
The apothem and radius of a square form a
45-45-90 triangle
The apothem of a square equals
1/2 a side
or
1/2 the radius X square root 2
Regular polygons having the same number of sides are
similar
An equilateral polygon inscribed in a circle
is a regular polygon
In an equilateral triangle, the apothem is
1/3 the altitude
Circumference=
pi(diameter)
or
2(pi)(radius)
For a regular polygon of n sides: Each interior angle i measures
(n-2)180/n
The area of a minor segment of a circle equals
the area of its sector less the area of the triangle formed by its radii and chord
The apothem and the radius of a hexagon form
30-60-90 Triangles
In the regular hexagon, square, and equilateral triangle, what kind of figures are formed.
Special right triangles are formed when the apothem r and a radius R terminating in the same side are drawn.
The length of a side in an equilateral Triangle equals
Radius X square root 3
The apothem and radius of an equilateral triangle form
30-60-90 Triangles
Radii of a regular polygon are
congruent
Segment of a circle
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.
In an equilateral triangle, the Radius is
2/3 the altitude
An apothem of a regular polygon
bisects the side to which it is drawn.
A circle may be circumscribed about
any regular polygon
For a regular polygon of n sides: Each central angle C measures
360/n
The center of the circumscribed circle of a regular polygon is also
the center of its inscribed circle
The length of a side of a regular hexagon equals
the length of the radius
A radius of a regular polygon
bisects the angle to which it is drawn
Area of a sector of n degree
Area of the Circle
=
length of an arc of measure n degree
Circumference of the circle
=
n/360
In a circle of radius r, the area K of a sector of measure n degree equals
n/360 of the area of the circle or
K=n/360 X piR^2
The side of a square equals
radius X square root 2
In an equilateral triangle, the apothem equals
1/2 the Radius
Areas of regular polygons having the same number of sides are to
each other as the squares of the lengths of any two corresponding segments
Apothems of a regular polygon are
Congruent
