Geometry

Question 1

Area of a Triangle

Answer 1

area = ½ base × height

Question 2

Angles in a Triangle

Answer 2

All angles in a triangle
sum to 180

x + y + z = 180

Question 3

Pythagorean Theorem

Answer 3

In a right triangle, a2 + b2 = c2,
where a and b are the legs
(shorter sides) and c is the
hypotenuse.

Question 4

Pythagorean Triples

Answer 4

The most common triples are 3–4–5,
5–12–13, 7–24–25, and 8–15–17.

Question 5

Similar Triangles

Answer 5

Similar triangles have all the
same angles, and sides that
are proportionate.

Question 6

Third Side Rule

Answer 6

The third side of a triangle is greater than
the difference of the other two sides and
less than their sum.
(a + b) > c > (b − a)

Question 7

Angle/side Relationship

Answer 7

Side length corresponds with
angle size. Angle z and side c are
the largest. Angle x and side a
are the smallest.

Question 8

Special Right Triangles

Answer 8

Question 9

Isosceles and Equilateral

Answer 9

equilateral = all sides are the same length
isosceles = two sides are the same length

In an equilateral triangle, all angles are 60°.

Question 10

Area of a Rectangle

Answer 10

area of a rectangle = length × width
area of a square = side2

Question 11

Area of a Parallelogram

Answer 11

area of a parallelogram = base × height

Question 12

Sum of Angles in a Polygon

Answer 12

sum of angles in a polygon = 180(n − 2),
where n = number of sides

Question 13

Volume and Surface Area of a Box

Answer 13

volume = l × w × h
surface area = 2lw + 2wh + 2lh

Question 14

Volume and Surface Area
of a Cylinder

Answer 14

volume = πr2h
surface area = 2πr^2 + 2πrh

Question 15

Lines and Angles

Answer 15

All angles in a line add up to 180°
x + y = 180

Question 16

Parallel Lines

Answer 16

When a line intersects with two parallel angles, the resulting intersections are identical.

Question 17

Intersecting Lines

Answer 17

When two lines intersect, opposite angles are equal.

Question 18

Distance and Midpoint on a Coordinate Plane

Answer 18

If you have endpoints (x1, y1) and
(x2, y2) of a line on a coordinate plane:

Question 19

Sector

Answer 19

Sector area and arc length are proportional to angle size. Here, the angle is 60°.

Since there are 360° in a circle, the sector (grey area) takes up 1/6 of the circle. Thus,
its area is 1/6 of the total area, and its arc length is 1/6 of the circumference.

Question 20

Slope, x-, y-intercept

Answer 20

y = mx + b, where m = slope, b = y intercept

slope = rise/run or (y2-y1)/(x2-x1)

The y-intercept is the y-coordinate on
a line at which x = 0.
The x-intercept is the x-coordinate on
a line at which y = 0.

Question 21

Circles Facts

Answer 21

diameter = 2r
circumference = πd or 2πr
area = πr2

Question 22

Central Angle (circles)

Answer 22

A central angle has a vertex that
lies at the center point of the
circle. An inscribed angle has its
vertex on the circle itself rather
than on the center of the circle.
An inscribed angle is equal to
half of the arc it intercepts.

Question 23

Triangles in Circles

Answer 23

If one of the sides of an
inscribed triangle is a diameter
of the circle, then the triangle
must be a right triangle.

Question 24

Coordinate Plane

Answer 24

• Slope: (change in y / change in x) (rise / run)
• Slope-intercept: y = mx + b
• “Line contains point” means you could plug a coordinate pair, f.e. (5, d)
  into a line, f.e. y = 3x + 4, by replacing x = 5 and y = d … d = 3(5) + 4
• parallel lines (do not intersect … same slope)
• perpendicular lines (slope is opposite reciprocal .. the product of their
  slope is -1)
• finding distance between two points (make a right. triangle where the
  distance is the hypotenuse)

Question 25

Lines/Angles

Answer 25

• angles on a line add up to 180º
• when two lines are parallel, all the small angles are the same, and all the
  big angles are the same
• if we’re told lines are parallel, find the clone angles

Question 26

Circles/Cylinders

Answer 26

• d = 2r Circ = π*d Area = π * r^2
• Arclength = (angleº / 360º) *circumfer.
• Area of sector = (angleº / 360º) * Area
• Capacity of cylinder: Vol = π r^2 * h
• Volume of liquid: Vol = π r^2 * h (of liquid)
• Rectangle inscribed in circle? Diagonal = Diam
• Circle inscribed in square? Diameter = Side
• Triangle inscribed in semi-circle? Right triangle.
• Two of triangles sides are radii? Isosceles

Question 27

Polygons

Answer 27

• Triangles have 180º. Every time you add a side, you add another 180º.
  n – 2 * 180 = total degrees (4 sides: 360º, 5 sides: 540º, 6 sides: 720º ..)
• Area of Trapezoid = (Avg. of Bases) * Height
• Area of Rhombus = ½ (product of diagonals)
• Volume of a Rectangular Solid: Vol = lwh
• Diagonal of Rectangular Solid: a^2+b^2+c^2 = d2
• Volume of Cube: Vol = s^3

Question 28

Triangles/Diagnoles

Answer 28

• 4 Special Right Triangles:
  3:4:5 / 5:12:13 / 45-45-90 (x : x : x√2) / 30-60-90 (x : x√3 : 2x)

√2 = approx. 1.4 (2/14)
√3 = approx. 1.7 (3/17)

• Diagonal of square = hypotenuse of 45-45-90
• Two equal sides <—> Two equal angles
• Area of equilateral triangle = (s^2 * √3) / 4 (or break into two 30-60-90 and solve that way)
• Difference < 3rd side of a triangle < Sum
• Exterior angle rule (if an angle is supplemental to one of a triangle’s three
  angles, it’s equal to the sum of the triangle’s other two angles.)
• SIMILAR TRIANGLES (triangles with the same set of three angles will
  have proportionate sides) .. this usually occurs when there are mini triangles
  within bigger triangle