Geometry

Question 1

distance from a point to the origin on a cordinate plane

Answer 1

√[(x-0)² + (y-0)²]

√X² + Y²

Question 2

The third side of a triangle must be…

Answer 2

less than the sum of the other two sides and greater than their difference

Question 3

sum of interior angles of a polygon

Answer 3

(n-2) x 180

Question 4

area of a triangle

Answer 4

(base x height) /2

Question 5

area of a rectangle

Answer 5

length x width

Question 6

area of a trapezoid

Answer 6

(base₁+ base₂) x height / 2

Question 7

area of a parallelogram

Answer 7

base x height

Question 8

area of a rhombus

Answer 8

diangonal₁ x diagonal₂ / 2

Question 9

surface area

Answer 9

the sum of all the areas of all the faces

Question 10

volume of a cube

Answer 10

s³

Question 11

volume of a rectangular solid

Answer 11

length x width x height

Question 12

how many books each with x volume can be packed into a crate with y volume

Answer 12

cannot be determined without knowing the exact dimension of the books

Question 13

the sum of angles of a triangle

Answer 13

180

Question 14

if you are given two sides of a triangle, the length of the 3rd side…

Answer 14

must lie between the difference and the sum of the two given sides

Question 15

common right triangles

Answer 15

3-4-5 (6-8-10, 9-12-15, 12-16-20)

5-12-13 (10-24-26)

8-15-17

Question 16

45º-45º-90º triangle

Answer 16

1 : 1 : √2

x : x : x√2

this triangle is exactly half of a square

Question 17

30º- 60º - 90º

Answer 17

1 : √3 : 2

x : x√3 : 2x

Question 18

diagonal of a square

Answer 18

d = s√2

Question 19

main diagonal of a cube

Answer 19

s√3

Question 20

deluxe pythagorean threorem to find diagonal of a rectangular solid

Answer 20

d² = x² + y² + z²

Question 21

similar triangles (define)

Answer 21

triangles are defined as similar if all their corresponding angles are equal and their corresponding sides are in proportion

Question 22

if two similar triangles have corresponding side lengths in ratio a:b, their areas will be…

their volumes will be…

Answer 22

a² : b²

a³ : b³

Question 23

special properties of equilateral triangles

Answer 23

can be split into two 30-60-90 triangles with the height of

(x√3)/2

area = (1/2)*S*(S√3/2)

=S²(√3/4)

Question 24

On DS questions regarding the xy-plane, we can use any
of the following to find the others:

Answer 24

1. Any single equation containing both x and y
2. Slope-intercept form of the line
3. Two points on the line
4. The intercepts of the line