Geometry

Question 1

vertices (polygons)

Answer 1

endpoints of the sides that meet

Question 2

how many triangles can a polygon be divided into

Answer 2

n-number of sides

n-2

Question 3

how to find sum of interior angles of a polygon

Answer 3

(n-2)(180º)

Question 4

Regular polygon

Answer 4

all sides and all angles are congruent

Question 5

How to find the angles of a regular polygon when you know the sides

Answer 5

(n-2)(180) = x

x/n = degree of each angle

Question 6

Triangles

Answer 6

sum of interior angles = 180º

length of each side is less than the sum of the other 2 sides

Question 7

equilateral triangle

Answer 7

3 congruent sides

3 congruent angles (60°)

Question 8

isosceles triangle

Answer 8

2 congruent sides

angles opposite the congruent sides are congruent

Question 9

right triangle

Answer 9

has interior right angle

hypotenuse is the side opposite the right angle

other sides are legs

Question 10

Pythagorean theorem

Answer 10

hypotenuse² = leg1² + leg2²

Question 11

ratio of sides of an isosceles right triangle

Answer 11

1 : 1: √2

y² = x^{2 +} x²

y² = 2x²

y = √2x

Question 12

30° 60° 90° triangle

Answer 12

half of an equilateral triangle

Question 13

ratio of sides of a 30-60-90 triangle

Answer 13

1: √3: 2

x² + y² = (2x)²

x² + y² = 4x²

y² = 3x²

y = √3x

Question 14

Area of triangle

Answer 14

A = (bh)/2

base x height

• any side can be the base
• height is a perpendicular line from base to opposite vertex

Question 15

3 ways to tell if two triangles are congruent

Answer 15

1. if 3 sides of one triangle are congruent to the other
2. if 2 sides and its angle are congruent on each
3. if 2 angles and a side are congruent

Question 16

similar triangles

Answer 16

same shapes but not necessarily the same size

you can match up the vertices so the angles are congruent

OR

the lengths of corresponding sides have the same ratio

(all 30-60-90° triangles are similar)

Question 17

proportions of similar triangles ABC and DEF

Answer 17

AB = BC = AC

DE = EF = DF

Question 18

sum of interior angles of a quadrilateral

Answer 18

360°

Question 19

rectangles

Answer 19

4 right angles

opposite sides are parallel and congruent

2 interior diagonals are congruent

if all four sides are congruent its a square

Question 20

parallelogram

Answer 20

both pairs of opposite sides are parallel

opposite sides are congruent and opposite angles are congruent

Question 21

trapezoid

Answer 21

2 opposite sides are parallel

A = 1/2 (b₁ + b₂)(h)

bs are corresponding sides

Question 22

Area of all parallelograms

Answer 22

A=bh

any side can be base

height is perpendicular line reaching to the other side

Question 23

Diameter =

Answer 23

2r

radii

Question 24

radii of congruent circles

Answer 24

equal radii

Question 25

chord

Answer 25

any line segment joining to points on the circle

Question 26

circumference

Answer 26

distance around the circle C/d = π or C = dπ or C = 2πr

Question 27

finding the length of an arc on a circle

Answer 27

ratio of arc length to circumference are the same as the ratio of inner arc degree to 360° _length of arc ABC_ = _arc°_ circumference = 360°

Question 28

Area of a circle

Answer 28

πr²

Question 29

tangent

Answer 29

line that intersects a circle at exactly one point radius is perpendicular to tangent lines

Question 30

rule about triangles inscribed in circles

Answer 30

if one side of an inscribed triangle is a diameter of the circle then the triangle is a right triangle (vice versa: a right triangle inscribed inside of circle then one side of it is the diameter)

Question 31

rectangular solids

Answer 31

6 faces 12 edges 8 vertices

Question 32

volume of rectangular solid

Answer 32

V = l x w x h

Question 33

surface area of a rectangular solid

Answer 33

sum of face areas A = 2 (lw + lh + wh)

Question 34

cube

Answer 34

6 square faces l = w = h

Question 35

Axis of cylinder

Answer 35

line that joins the 2 centers of the circles (its height)

Question 36

right circular cylinder

Answer 36

axis is perpendicular to bases

Question 37

volume of cylinder

Answer 37

V = πr²h

Question 38

Surface area of cylinder

Answer 38

(2πr²) + 2πrh