Geometry

Question 0

Ratio of sides for a 45-45-90 triangle?

Answer 0

X : X : X(sq rt 2)

Question 1

3 common Pythagorean triples

Answer 1

3 - 4 - 5

5 - 12 - 13

8 - 15 - 17

Question 2

Ratio of sides for 30-60-90 triangle

Answer 2

30 - x
60 - x (sq rt 3)
90 - 2x

Question 3

Area of triangle

Answer 3

1/2(base) x height

Question 4

Area of trapezoid

Answer 4

(Base1 + Base2) / 2 x height

Question 5

Area of a circle

Answer 5

pie (radius^2)

Question 6

How do you find slope of a line?

Answer 6

Rise/run or change in y over change in x. Need 2 point (x1,y1) (x2,y2)

Question 7

Equation for a line in slope - intercept form

Answer 7

Y =mx + b

M = slope
B = y-intercept (where x=0)

Question 8

Area of parallelogram

Answer 8

Base x height

Question 9

Circumference of a circle

Answer 9

pie (diameter)

2r (pie)

Question 10

Slope and slope of perpendicular line

Answer 10

Slope = m

Perpendicular slope = (- 1/m)

Question 11

Two sides of a triangle are 4 and 10. If the third side is an integer x. How many possible values are there for x?

Answer 11

X must be greater than 10-4 and less than 10 + 4

So 7,8,9,10,11,12,13

Question 12

Deluxe Pythagorean theorem

Answer 12

D^2= x^2 + y^2 + z^2 where x, y and z are the sides of a rectangular solid and d is the main diagonal.

Question 13

What defines similar triangles?

Answer 13

If corresponding angles are equal and corresponding sides are in proportion.

Once you find 2 triangles and 2 pairs of equal angles = similar

Question 14

Area of equilateral triangle with side length S=

Answer 14

(S^2)(sq rt 3) / 4

Question 15

Diagonal of a square with side length s

Answer 15

S(sq rt 2)

Question 16

Diagonal of cube with edge length s

Answer 16

S(sq rt 3)

Question 17

What is an inscribed angle in a circle? VS. central angle

Answer 17

An inscribed angle has it’s vertex on the line of the circle.
A central angle’s vertex lies at the center point of a circle.
An inscribed angle is 1/2 the arc it intercepts

Question 18

Proof needed to show that quadrilateral is a square

Answer 18

1) diagonals bisect each other

2) one right angle

Question 19

Definition of parallelogram

Answer 19

Opposite sides =

Opposite angles =

Question 20

Definition of rectangle

Answer 20

All angles = 90

Opposite sides equal

• a rectangle is a special type of parallelogram
• a square is a special type of rectangle

Question 21

Definition of rhombus

Answer 21

All sides =
Opposite angles are equal

• rhombus is a special type of parallelogram
• square is a type of rhombus

Question 22

Volume of cylinder

Answer 22

Pie (r^2)(h)

Question 23

What is isosceles triangle?

Answer 23

Triangle in which 2 sides are equal

45-45-90

X-X-X(sq rt 2)

Question 24

Distance between 2 points (x1,y1) and (x2,y2)

-2,9) and (-7,-3

Answer 24

Sq rt ( (x-x)^2 + (y-y)^2)

13

Question 25

Surface area of a cylinder

Answer 25

2(pie)r^2 + 2(pie)rh

R- radius
H- height

Question 26

Volume of cylinder

Answer 26

(Pie)(r^2)(h)

Question 27

Perpendicular slopes

Answer 27

2 lines that are perpendicular have slopes that are negative reciprocal i.e. when product of slopes is -1

Question 28

A quadrilateral has a perimeter of 36 inches.

What shape results in maximum area?

Minimum area?

Answer 28

9 x 9 square has max area

1 x 17 rectangle has min area

Question 29

Given a fixed area value, what shape has minimum perimeter?

Answer 29

Square had minimum perimeter (or other polygon w/ right angles)

Question 30

Given two sides of a triangle or parallelogram, how do you maximize area?

Answer 30

Place sides perpendicular

Question 31

Proof needed for similar triangles

Answer 31

2 angles equal.

Similar triangles have all angles equal and all angles in proportion.

Question 32

Relationship btw side lengths and areas of similar triangles

Answer 32

If sides are in ratio of a:b then their areas will be in ratio of a^2:b^2

Question 33

Circ of a circle

Answer 33

2(pie)(r)