Geometry

Question 1

Area of a circle

Answer 1

a=pi X radius squared

Question 2

circumference of a circle

Answer 2

c=d(pi) c=2r(pi)

Question 3

what is a sector and its circumference

Answer 3

sector= fractional portion of a circle, its circumference is equal to c=dxpi x its fraction

Question 4

what is a central angle? how do you find the fraction?

Answer 4

the angle coming off of a circle’s center. it will give you the portion of the fraction of the sector. (degree between two radii).
if you have the degrees of the angle, divide it by 360 to get the fraction of the sector to circle. eg 90/360= 1/4 of the circle

Question 5

how can you solve for sector fraction or variables?

Answer 5

know any of these values: central angle/360 = sector area/circle area= arc length/circumference

Question 6

triangle properties: what do you know about sides?

Answer 6

the sum of two sides of a triangle> length of 3rd side. distance between two corners is the straight line between them.
any side is greater than the difference of the two other sides
perimeter: sum of sides of the triangle

Question 7

triangle properties: what do you know about angles

Answer 7

sum of all the angles=180

Question 8

triangle properties: what do you know about angles and sides

Answer 8

the largest side is always across the largest angle, the smallest side across from the smallest angle.

isosceles triangle: has 2 equal angles and 2 equal sides

equilateral triangle has 3 equal angles and sides. angles are 60 degrees each

Question 9

area of a triangle

Answer 9

A=.5(b x h) b and height have to be perpendicular to each other (right angle)

Question 10

find the third side of a right triangle.

What are the common right triangle triplets? memorize them!

Answer 10

pythagorean theorem: a(a)+b(b)=c(c) a and b are the legs of the right angle.

3-4-5
5-12-13
8-15-17 
6-8-10
10-24-26
*can double, triple or apply a common multiplier to these!

Question 11

quadrilaterals: what do you know about them?

Answer 11

figure with 4 sides

- can always split into two triangles

Question 12

parrallelograms: what do you know about them?

Answer 12

the opposite sides are parallel and equal.
opposite angles are also equal
adjacent angles add up to 180
can split it into two equal triangles
diagonals also cut each other in half
perimeter= sum of all sides
area: b x h (b and h have to be perpendicular)

Question 13

If a side of a triangle intersects the center of a circle, What do you know about the side and what type of triangle is it?

Answer 13

The side is the diameter
The triangle is a right triangle.
The angle opposite of the side is a right angle.

Question 14

What are the three properties of intersecting lines?

Answer 14

The four angles created are a circle so sum is 360

Each pair of angles that form a line equal 180.

The angles that are opposite of each other are equal.

Question 15

What are two important relations of a triangle’s sides to it’s angles?

Answer 15

The largest angle points to the largest side.

If two sides are equal than the opposite angles are equal

Question 16

What is the equation to find the sum of the angles of a polygon?

Answer 16

(n-2)x180

n=number of sides

Question 17

What is the sum of the angles of a triangle?

Answer 17

180

(3-2)180=180

Question 18

What is the sum of the angles of a quadrilateral?

Answer 18

(4-2)180=360

Question 19

What is the sum of the angles of a pentagon?

Answer 19

(5-2)180=540

Question 20

What is the sum of the angles of a hexagon?

Answer 20

(6-2)180=720

Question 21

What is the relationship between the sides of a triangle?

Answer 21

The sum of two of the sides is greater than the 3rd side. The difference of two of the sides will always be less than the 3rd side. Cannot be equal

Question 22

What is the relationship between the 3 sides of a right triangle?

Answer 22

Pythagorean theorem

a^2 + b^2 = c^2

Question 23

What are the 3 most common right triangles?

Answer 23

3: 4:5
5: 12:13
6: 8:10
8: 15:17

Question 24

What is the right triangle side ratio of a 45:45:90 right triangle?

Answer 24

X : X : Xsqrt(2)

Question 25

What is the side ratio of a right triangle that has angles of 30:60:90?

Answer 25

X : Xsqrt(3) : 2X

Question 26

What is the diagonal of a square?

Answer 26

xsqrt(2)

Question 27

What is the diagonal of a rectangle?

Answer 27

2x or C in a^2 + b^2 = c^2

Question 28

What can you tell when you have a transversal ?

Answer 28

There are 8 angles but only two angle measurements. All acute angles are equal and all obtuse angles are equal

Question 29

Parallelogram

Answer 29

Opposite sides and opposite angles are equal

Question 30

Rectangle

Answer 30

All sides are 90 degrees and opposite sides are equal

Question 31

Square

Answer 31

All sides are equal. All angles are 90

Question 32

Trapezoid

Answer 32

One pair of opposite sides is parallel.

Question 33

Area of a trapezoid

Answer 33

(Base 1 + base 2)/2 x height

Question 34

What are common multiples of right triangle 3-4-5?

Answer 34

3-4-5
6-8-10
9-12-15
12-16-20

Question 35

What is a common multiple for 5-12-13 triangle?

Answer 35

10-24-26

Question 36

What is a common right triangle beside 3:4:5 and 5:12:13?

Answer 36

8:15:17

Question 37

What triangle is closely related to 30:60:90 triangle and why?

Answer 37

Equilateral triangle. when you split it in half you get two 30 60 90 triangles

Question 38

What is the relation between a central angle and it’s arc?

Answer 38

The degrees are equal and it represents a section of the whole circle.

Question 39

What is the relation of an inscribed angle (not a central angle) and it’s arc?

Answer 39

The angle’s degrees are half of the arc’s degrees.

Question 40

What is the surface area of a cylinder?

Answer 40

2(R^2)pi + H(2rpi)

Question 41

What is the equation for a line’s slope?

Answer 41

rise/run. Yb-Ya/Xb-Xa

Question 42

What are the four types of slopes?

Answer 42

Positive
Negative
Undefined (vertical)

Zero (horizontal)

Question 43

What is the slope of a perpendicular bisector?

Answer 43

the negative reciprocal