Geometry

Question 1

Triangle (Formulas)

Answer 1

perimeter = sum of the lengths of the 3 sides

area = base*height/2
height of a right triangle is shortest side, if not a right triangle you must draw in height

pythagorean theorem: a^2 + b^2 = c^2

Question 2

Pythagorean Triples

Answer 2

3: 4: 5
5: 12: 13
7: 24: 25
8: 15: 17
9: 40: 41

Question 3

Right Triangle 30-60-90 proportions

Answer 3

x: x√3: 2x

Question 4

Right Isosceles Triangle 45-45-90 proportions

Answer 4

x: x: x√2

Question 5

Axis

Answer 5

y axis is vertical

x axis is horizontal

Question 6

Standard form of a line

Answer 6

y = mx + b 
m = slope
b = y-int

Question 7

Slope

Answer 7

Δ y / Δ x

rise/run = y2 -y1 / x2 - x1

parallel lines have same slope
perpendicular lines have negative reciprocal slope

Question 8

Lines and Angles

Answer 8

• vertical angles are equal
• the sum of angles that form a straight line = 180
• when two parallel lines are intersected by a third line (transversal), the corresponding angles are equal

Question 9

Polygons

Answer 9

• formed by 3 or more line segments
• (n-2)180 = the sum of the interior angle measures of a polygon with n sides
• perimeter = sum of sides

Question 10

Triangles

Answer 10

• interior angles sum to 180
• every external angle of a triangle equals the sum of the 2 noncorresponding internal angles
• in any triangle, a side opposite a greater angle is longer than a side opposite a smaller angle, and sides opposite equal angles are equal
• every side of triangle must be longer than the difference of the lengths of the other 2 sides
• equilateral: sides are equal, angles equal
• isosceles: 2 sides of equal length (opposite angles of the equal sides are equal)
• right: one angle equals 90, longest side of triangle is opposite 90 angle (hypotenuse)
• pythagorean triples for right triangles only

Question 11

Parallelogram (includes rectangles and squares)

Answer 11

height won’t be the side of the figure (may have to draw in)

• opposite sides equal so opposite angles equal
• area = bh
• perimeter = sum of all sides

Question 12

Trapezoid

Answer 12

area = 1/2 (b1 + b2)h

Question 13

Circle

Answer 13

• area = TTr^2
• circumference = TTd
• arc length = 1/n(circumference), where n is the fraction of the portion of circle n/360
• area of sector = 1/n(area)
• triangle is inscribed in semicircle when one its sides is diameter of circle, with other 2 sides meeting at any point on circle (inscribed triangles always right triangles)

Question 14

Multiple figures

Answer 14

• break the figures down to simpler figures

- look for SHARED measurements

Question 15

Solids

Answer 15

volume = l x w x d (rectangle, cube)
volume = area of base x depth
- cylinder = TTr^2 (depth)
surface area = sum of ALL areas from ALL faces

Question 16

Coordinate geometry

Answer 16

• every point has ordered pair (x,y)
• able to find m if you know any 2 point on the line
• one way to find distance in coordinate plan is with pythagorean theorem (note special right triangles)

Question 17

Rule of triangles

Answer 17

Every side must be larger than the difference between the other two sides and shorter than their sum