Geometry

Question 1

When one shorter side of a right triangle has a length of (a multiple of) 3 and the other shorter side has a length of (a multiple of) 4, what must the length of the hypotenuse be (a multiple of)?

Answer 1

(A multiple of) 5

3-4-5 right triangle

Question 2

When one shorter side of a right triangle has a length of (a multiple of) 5 and the other shorter side has a length of (a multiple of) 12, what must the length of the hypotenuse be (a multiple of)?

Answer 2

(A multiple of) 13

5-12-13 right triangle

Question 3

What is an isosceles triangle?

What is an isosceles right triangle?

Answer 3

A triangle that has 2 equal sides and 2 equal angles.

An isosceles right triangle has two equal sides and two equal angles that each measure 45 degrees. The third angle measures 90 degrees.

Question 4

What are the two shorter sides of a right triangle?

Answer 4

The legs - also the base and the height of the triangle

Question 5

What is the area of a triangle?

Answer 5

(base x height) / 2

Question 6

What is the area of a right triangle?

What about the area of an isosceles right triangle?

Answer 6

(Leg 1 x leg 2) /2

(Leg^2)/2 -> since the legs are the same length

Question 7

The sides of a right isosceles triangle (or 45-45-90 triangle) will always be in what ratio?

Answer 7

x, x, root 2* x

Question 8

What’s important to know when asked to find the diagonal of a square?

Answer 8

The diagonals of a square cut the square into two 45-45-90 right triangles. The area of each of these triangles is half of the area of the square that they form. Thus if you are given 1 side of the square, you can find the length of the diagonal.

Question 9

The sides of a 30-60-90 triangle will always be in what ratio?

Answer 9

x:x*root3:2x

Where x is the length of the side opposite the 30 degree angle and x*root3 is the length of the slide opposite the 60 degree angle, and 2x represents the hypotenuse

Question 10

What is the area of an equilateral triangle?

Answer 10

(S^2*root3)/4

Question 11

Dropping an altitude from the upper vertex to the base of an equilateral triangle produces what?

Answer 11

2 identical 30-60-90 triangles

Question 12

What are the 3 ways triangles can be similar?

Answer 12

1) the 3 angles of 1 triangle are the same measure of the three angles of another triangle
2) the three pairs of corresponding sides have lengths in the same ratio
3) an angle of one of the triangles is the same measure as an angle of another triangle and the sides surrounding these angles are in the same ratio

Question 13

What is a quadrilateral?

Answer 13

A four sided polygon: square, rectangles, parallelograms, rhombuses, and trapezoids

Question 14

All square are….

Answer 14

Rectangles

Question 15

All rectangles are…

Answer 15

Parallelograms

Question 16

What is the area of a parallelogram?

Answer 16

base x height (the height is always perpendicular to the base)

Question 17

What is a rectangle and what is the area of a rectangle?

Answer 17

Any quadrilateral with 4 right angles / a rectangle is also a parallelogram so opposite sides are equal

Length x width

Question 18

The exterior angles of any polygon sums to what?

Answer 18

360 (take only 1 exterior angle per vertex)

Question 19

What is the longest chord in a circle?

Answer 19

The diameter of the circle

Question 20

What is the area of a circle?

Answer 20

pi*r^2 or pi(d/2)^2

Question 21

What is the circumference of a circle?

Answer 21

2pir or pi*d

Question 22

What is important to know about circles inscribed in equilateral triangles?

Answer 22

Each point at which the circle touches the triangle is the midpoint of the side of the triangle

By drawing a segment from the centre of the circle to the base of the triangle, two 30-60-90 triangles are created

Question 23

How do you calculate the diagonal of a square?

Answer 23

Root 2 * length of a side

Question 24

When a square is inscribed in a circle, a diagonal of the square is also what?

Answer 24

The diameter of the circle

Question 25

When a circle is inscribed in a square, what must be true?

Answer 25

The diameter of the circle has the same length as a side of the square

Question 26

The area of an inscribed square will be smallest when what?

Answer 26

The vertices of that square are located at the midpoints of the respective edges of the circumscribed square. The area of such an inscribed square will be half of the area of the circumscribed square.

Question 27

In a two circle system, what is the area of the outer ring?

Answer 27

Pi * (R1^2 - R2^2) where RI is the radius of the outer circle and R2 is the radius of the inner circle

Question 28

What is the longest line segment that can be drawn within a rectangular solid?

Answer 28

d^2 = l^2 + w^2 + h^2

Question 29

What is the longest line segment that can be drawn within a cube?

Answer 29

d=s*root3

Question 30

What is the surface area of a cube?

Answer 30

6s^2

Question 31

What is the surface area of a rectangular solid?

Answer 31

2(LW) + 2(LH) + 2 (HW)

Question 32

How do you find the number of sides of a regular polygon when given the interior angle?

Answer 32

((n-2)180) / n = interior angle

Where n is the number of sides

Question 33

What is the area of a 30-60-90 triangle?

Answer 33

(x^2*root3)/2

Question 34

What is the perimeter of a 30-60-90 triangle?

Answer 34

x (3+root 3)

Question 35

What is the volume of a right circular cylinder?

Answer 35

pir^2h

Question 36

What is the surface area of a right circular cylinder?

Answer 36

2pir^2 + 2pir*h