Geometry

Question 1

When n lines intersect through a common point, the sum of the angles created by the those n lines is…

Answer 1

360

Question 2

Angles are supplementary if..

Answer 2

Angles are supplementary if their measures add up to 180°.

Question 3

For triangles, the longest side of the triangle is always opposite…

Answer 3

the largest angle

Question 4

For triangles, the shortest side of the triangle is always opposite…

Answer 4

the smallest angle

Question 5

Sum of several exterior ADJACENT angles of a polygon must equal…

NOT mirroring angles

Answer 5

360

taking one exterior angle at each vertex. if more than one, treat each additional as another part of a 360 add up

Question 6

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

Answer 6

‘remote’ angles are those that are not immediately next to exterior angles

Question 7

Sum of lengths of any two sides of a triangle must…

Answer 7

Be greater than the length of the third size

A + B > C

B + C > A

A + C > B

Question 8

Difference of lengths of any two sides of a triangle must…

Answer 8

Be less than the length of the third size

A - B < C

B - C < A

A - C < B

Question 9

Acute angle is

Answer 9

less than 90 degrees

Question 10

obtuse angle is

Answer 10

greater than 90 degrees but less than 180

Question 11

Two most common pythagorean triples

Answer 11

3-4-5 [incl any multiples such as 6,8,10 and 9,12,15]
5-12-13 [incl any multiples as as 10,24,26]

Question 12

what are the angles of an isosceles right triangle

Answer 12

45-45-90

2 legs are equal

area = leg^2/2

Question 13

Ratio of sides of 45-45-90 right triangle [iscoeles]

Answer 13

x : x : x√2

where x is the length of the two equal legs, x√2 is hypotenuse

if we know the size of one leg, we can determine the size of all legs

Question 14

Ratio of sides of 30-60-90 right triangle

Answer 14

x : x√3 : 2x

x = side opposite of 30 degree angle

x√3 = side opposite of 60 degree angle

2x = side opposite of 90 degree angle

if we know the size of one leg, we can determine the size of all legs

Question 15

Area for equilateral triangle

Answer 15

Area=s^2√3/4

where s is one size

the area can only be determined only when the height is known

Question 16

What are quadrilaterals?

Answer 16

four sided polygons, including squares, rectangles, parallelograms, rhombuses, and trapezoids

all squares are rectangles, all rectangles are parallelograms

Question 17

what is the equation for the diagonal of any rectangle?

Answer 17

√l^2+w^2

Question 18

Properties of a square

Answer 18

• 4 right angles
• 4 sides of equal length
• each diagonal bisects the square into 2 45-45-90 triangles
• length of square’s diagonal [hypotenuse] = s√2 where s is the length of one side of square

Question 19

Given a rectangle with a fixed perimeter, the rectangle with the maximum area is a square.

Answer 19

Given a rectangle with a fixed perimeter, the rectangle with the maximum area is a square.

Question 20

Given a rectangle with a fixed area, the rectangle with the smallest perimeter is a square.

Answer 20

Given a rectangle with a fixed area, the rectangle with the smallest perimeter is a square.

Question 21

Trapezoid

Answer 21

Trapezoid is a quadrilateral where the bases are parallel but the other pair of opposite sides are not parallel

Question 22

area of a trapezoid

Answer 22

(base 1 + base 2) * height / 2

Question 23

sum of interior angles of a polygon

Answer 23

sum of interior angles of polygon = (n-2) x 180

where n = number of sides

Question 24

measure of any one interior angle in a polygon

Answer 24

180(n-2)/n

Question 25

Hexagon

Answer 25

• six equal sides and six equal angles
• interior angles add up to 720 degrees
• each interior angle measures to 120 degrees

Question 26

Area of a hexagon

Answer 26

3√3/2 * (s^2) where s is length of one of the sides

Question 27

How to label the quadrants of the XY plane

Answer 27

start in top right corner with I and go counter-clockwise with 2, 3, 4

Question 28

Slope of a line formula

Answer 28

y2 - y1 / x2 - x1

Question 29

Slope of a line

Answer 29

The slope of a line can be
- zero (a horizontal line)
- undefined (a vertical line)
- positive (a line that rises when the line moves from left to right)
- or negative (a line that falls when the line moves from left to right).

Question 30

what is an intercept?

Answer 30

Point where line crosses the x and y axises

Question 31

Lines with positive slopes - golden rule

Answer 31

will always intersect quadrants I and III

Question 32

Lines with positive slopes - x intercept is negative

Answer 32

y intercept is positive, will intersect quadrants I, II, III

Question 33

Lines with positive slopes - x intercept is zero

Answer 33

will only intersect quadrants I and III

Question 34

Lines with positive slopes - x intercept is positive

Answer 34

y intercept is negative, will intersect quadrants I, III, IV

Question 35

3 equivalent circle ratios

Answer 35

central angle / 360 = arc length/circumference = area of sector / area of circle

Question 36

Angles inscribed in a circle

Answer 36

The degree measure of an inscribed angle is equal to half of the degree measure of the arc that it intercepts.

Question 37

The legs of an isoceles triangle can be the radii of a circle

Answer 37

if legs start at beginning of circle and end at circumfrence, it is an isoceles triangle with equal legs 45-45-90

Question 38

If an equilateral triangle is inscribed in a circle, the center of the triangle is the center of the circle

Answer 38

a line drawn from the center of the triangle to a vertex of the base creates a 30-60-90 triangle. the line would also create a radius

Question 39

What is midpoint formula for a coordinate graph

Answer 39

X1+X2/2 and Y1+Y2/2

basically finding average of both points

Question 40

Distance between two points formula

Answer 40

d=√((x2 – x1)² + (y2 – y1)²).

Question 41

y = mx + b

Answer 41

y = y point of (x,y) pair
m = slope = y2-y1/x2-x1 or rise over run
x = x point of (x,y) pair
b = where the line crsses the y intercept [the vertical line]

Question 42

the slopes of two perpendicular lines will always multiply together to equal

Answer 42

negative 1

Question 43

if two lines are parallel, they have…

Answer 43

same slope