Geometry

Question 1

Complementary Angles

Answer 1

Two angles are complementary angles to each other if their measures equals 90 degrees.

Question 2

Acute angles measures less than 90 degrees.

Answer 2

Obtuse angles measures between 90 and 180 degrees.

Question 3

The sum of the interior angles of any triangle is always 180 degrees.

Answer 3

The sum of the exterior angles or any polygon is always 360 degrees.

Question 4

Equilateral Triangle

Equal sides and equal angles
All angles equal 60 degrees

Answer 4

Exterior angle theorem:

An exterior angle of a triangle is equal to the sum of the remote interior angles.

Question 5

The 3 exterior angles of any triangle add up to 360 degrees.

Answer 5

Triangle Inequality Theorem

The largest possible third side of a triangle must be smaller than the sum of the other two sides.

Question 6

Area of a triangle = 1/2 (Base) (Height)

Answer 6

Pythagorean theorem

For only all right triangles, the square of the hypotenuse is equal to the sum of the squares of the legs.

(Leg1)^2 + (Leg2)^2 = (Hypotenuse)^2
or
a^2 + b^2 = c^2

Question 7

There are 50 Pythagorean Triples, which are right triangles with the following ratios:

16 are primitive triplets with hypotenuse less than 100: (3, 4,5), (5, 12, 13), (8, 15, 17), (7, 24, 25), (20, 21, 29), (12, 35, 37), (9, 40, 41), (28, 45, 53), (11, 60, 61), (33, 56, 65), (16, 63, 65), (48, 55, 73), (36, 77, 85), (13, 84, 85), (39, 80, 89), and (65, 72, 97)

Question 8

Special Right Triangles

Isosceles right triangles (45, 45, 90 with a ratio of x : x : x square root of 2 ) and (30, 60, 90 with a ratio of x : x square root of 3 : 2x

These special triangles doesn’t require the pythagorean equation to solve.

Question 9

Quadrilaterals

A quadrilateral is a four sided polygon, regardless of a quadrilateral shape, the four interior angles sum up to 360 degrees.

Answer 9

A trapezoid is a quadrilateral with at least one pair of parallel sides.

Question 10

A parallelogram is a quadrilateral with two pairs of parallel sides. Opposite sides are equal in length; opposite angles are equal in measure; angles that are not opposite are supplementary to each other.

Answer 10

A rectangle is a parallelogram with four right angles. Opposite sides are equal; diagonals are equal.

Question 11

A rhombus is a parallelogram with four equal size. Opposite angles are equal to each other, but they do not have to be right angles.

Answer 11

A square is a rectangle with equal sides, and equal angles.

Question 12

Perimeter of a Rectangle

Answer 12

perimeter = 2(Length + Width)

Question 13

Circumference of a Circle

Pi (π) is the constant ratio of the circumference of a circle to its diameter. It’s value is approximately 3.14

Answer 13

Circumference formula stated in terms of the radius:

C = 2(π)(r) or in terms of the diameter

C = π(d)

Question 14

Arc Length

Arcs are associated with central angles, they can be measured in degrees. The degree measure of an arc is equal to that of the central angle that cuts it off.

Answer 14

Arc length = n/360 (2πr) or n/360 (πd) ; where n is the degree of the arc

Question 15

Area of a Circle

Answer 15

Area of a circle = πr^2

Question 16

Area of a Sector

Answer 16

Area of a Sector = n/360 (πr^2) ;
where n is the degree and πr^2 is the area of a circle.

Question 17

Distance on the Coordinate Plane

Answer 17

If a line segment is parallel to the x-axis, the y-coordinate of every point on the line segment will be the same. If a line segment is parallel to the y-axis, the x-coordinate if every point on the line segment will be the same.

Therefore, to find the length of a line segment parallel to one of the axes, all you have to do is find the difference between the endpoint coordinates that do change.

Question 18

To find the length of a line segment that is not parallel to one of the axes by treating the line segment as the hypotenuse of a right triangle.

Question 19

Linear Equations

Answer 19

y = mx + b ;

where “m” is the slope of Δy/Δx (rise/run) and “b” is the point where the line intercepts the y-axis (y-intercept) and x = 0

Lines that are parallel to the x-axis have a slope of zero; there have the equation y = b. Lines that are parallel to the y-axis have the equation x = a, where a is the x-intercept of that line.

Question 20

Function Notation for a Line

Answer 20

f(x) = mx + b

As a parabola moves out along the x-axis in either direction, it grows vertically along the y-axis at a faster rate.

Question 21

Quadratic Function

Answer 21

f(x) = ax^2 + bx + c

If a is positive, the parabola opens up upward. If a is negative, the parabola opens ụp downward. “c” represents the vertical shift from the x-axis of the corresponding graph’s y-intercept. A c-value of -2 would mean that the parabola is shifted 2 units downward from the x-axis.

+/- constants from a function; right or left shift

x or / constants from a function; stretching or shirking

Multiplying a function by -1 results in the reflection of that function across the x-axis.

Question 22

Graphing Circles

Answer 22

r^2 = (x - a)^2 + (y - b)^2

r = radius
a = # of units that the circle’s center is shifted horizontally from the origin of the xy-plane.

b = # of units that the circle’s center is shifted vertically from the origin

ab = circle’s center point
x and y are points on the plane

Question 23

Surface Area of a Rectangular Solid

Sum of areas of faces = 2lw + 2lh + 2hw
or 2(wl + hl + hw)

Answer 23

Volume of a Rectangular Solid:

V = (Length x Width x Height)

Question 24

Volume of a Cube

Answer 24

Since a cube is a rectangular solid, for which length equals width equals height, the formula for its volume can be stated in terms of any edge:

Volume of a cube = lwh = (edge)(edge)(edge) = e^3

Surface area of a cube = sum of area of faces = 6e^2

Question 25

Volume of a Cylinder

Answer 25

Volume of a Cylinder = (area of base)(height) = πr^2h

Lateral Surface Area of a Cylinder = (circumference of base)(height) = 2πrh

Total Surface Area of a Cylinder = areas of circular ends + Lateral surface area = 2πr^2 + 2πrh

Question 26

Finding the Diagonal Length of a Rectangle

Answer 26

c^2 = a^2 + b^2

Question 27

Area of a Trapezoid

Answer 27

A = ((a + b) / 2) (h) ; where a and b is the bases and h is the height.

Question 28

Formula for Finding the Distance between to Endpoints

Answer 28

d = square root of (x2 - x1)^2 + (y2 - y1)^2

Question 29

Formula for Length of the Diagonal for any Cube or Rectangular Solid

Answer 29

d^2 = a^2 + b^2 + c^2

Question 30

Supplementary Angles

Answer 30

Two angles are complementary angles to each other if their measures equals 180 degrees.