Plane Geometry

Question 1

Plane geometry: adding and subtracting lengths

Answer 1

best way to start is to mark up the figure, put as much info from the question into the figure that you can. then plan and solve

Question 2

triangle

Answer 2

three sided polygon

Question 3

Sum of interior angles of triangles

Answer 3

all three angles equal 180

Question 4

Measure of an exterior angle of triangles

Answer 4

the measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

Question 5

sum of the exterior angles of triangles

Answer 5

the measure of three exterior angles of any triangle add up to 360 degrees

Question 6

area formula of a triangle

Answer 6

1/2(base)(height)

Question 7

what is the height of a triangle

Answer 7

the height is perpendicular distance between the side that’s chosen as the base and the opposite vertex

Question 8

triangle inequality theory

Answer 8

the length of any one side of a triangle must be greater than the positive difference and less than the sum of the lengths of the other two sides.

Question 9

Similar triangles

Answer 9

triangles that have the same shape: corresponding angles are equal and corresponding sides are proportional.

Question 10

three special triangles

Answer 10

isosceles, equilateral, and right triangles

Question 11

isosceles triangle

Answer 11

an isosceles triangle is a triangle that has two equal sides. Not only are two sides equal, but the angles opposite the equal sides, called base angles, are also equal.

Question 12

equilateral triangle

Answer 12

an equilateral triangle is a triangle that has three equal sides and equal angles.

Question 13

area of a equilateral triangle

Answer 13

s^2sqrt(3)/4 s being a side

Question 14

right triangle

Answer 14

a right triangle is a triangle with a right angle. the two sides that form the right angle are called legs

Question 15

Pythagorean theorem

Answer 15

you find the length of any side of a right triangle using a^2+b^2=c^2

Question 16

Pythagorean triplet

Answer 16

a set of integers that fits the Pythagorean theorem, the simplest is 3,4,5. any integers in a 3:4:5 ratio make up a triplet.

Question 17

hidden special triangles

Answer 17

key to solving a lot of geometry problems is to add a line segment or two to the figure. then find some special characteristics of triangles

Question 18

Trapezoid

Answer 18

a four-sided figure with one pair of parallel sides and one pair of nonparallel sides.

Question 19

area of a trapezoid

Answer 19

{(base1+base2)/2}x height

average of the parallel sides and the perpendicular side for height

Question 20

Parallelograms

Answer 20

a parallelogram is a four-sided figure with two pairs of parallel sides. opposite sides are equal, opposite angles are equal.

Question 21

area of parallelogram

Answer 21

base*height

Question 22

rectangle

Answer 22

a rectangle is a four sided figure with four right angles. opposite sides are equal.

Question 23

area of a rectangle

Answer 23

length * width

Question 24

Rhombus

Answer 24

a four sided figure with four equal sides (like a parallelogram but equal

Question 25

square

Answer 25

four sided figure with four right angles and for equal sides.

Question 26

area of square

Answer 26

(side)^2

Question 27

area of a hexagon

Answer 27

[3s^2sqrt(3)]/2

Question 28

circumference of a circle

Answer 28

the total distance around the circle.
=2pieR
=pieD
r radius and d diameter

Question 29

Length of an arc

Answer 29

an arc is a piece of the circumference. if n is the degree measure of the arcs angle then the formula is
(n/360)(2pieR)

Question 30

Area of a circle

Answer 30

pieR^2

Question 31

area of a sector

Answer 31

sector is a piece of the area of a circle.

n/360)(pieR^2