Geometry

Question 1

Pythagorean triplets

Answer 1

(2,3,4)

(5,12,13)

(8,15,17)

(9,40,41)

(11,60,61)

Question 2

For a given area the rectangle with the smallest perimeter is…

Answer 2

…a square.

Question 3

What is the average of the measures of the five angles of a pentagon?

Answer 3

3 triangles fit in a pentagon; 540 degrees/5=108

Question 4

In a 45-45-90 right triangle, the ratio of the sides are…

Answer 4

… x : x : xroot2

Question 5

In a 30-60-90 right triangle, the ratio of the sides are:

Answer 5

… x : xroot3 : 2x

Question 6

The area of a circle in terms of its circumference:

Answer 6

C²/4

Question 7

Where as the longest side of any triangle to be found?

Answer 7

Opposite its largest angle.

Question 8

The sum of the lengths of any two sides of a triangle is…

Answer 8

…greater than the length of the third side.

Question 9

The difference of the lengths of any two sides of a triangle is…

Answer 9

…less than the length of the third side.

Question 10

Similar triangles have…

Answer 10

…equal corresponding angles and their corresponding sides are proportional.

Question 11

If a line segment parallel to one of the sides of a triangle is drawn…

Answer 11

…the two triangles become similar.

Question 12

The sum of the measures of n angles in a polyton with n sides is…

Answer 12

…(n-2)*180

Question 13

The sum of the exterior angles of a polygon is…

Answer 13

360

Question 14

In a parallelogram consecutive angles add up to…

Answer 14

…180

Question 15

The two diagonals in a parallelogram…

Answer 15

…bisect one another.

Question 16

For any given area, the rectangle with the smallest perimeter is…

Answer 16

…a square.

Question 17

The area of a trapezoid is…

Answer 17

1/2(AB + CD)*h

Question 18

The ratio of the areas of two circles is…

Answer 18

…the square of the ratio of their radii

A₁/A₂ = r²1/r²2

Question 19

If an arc measures x⁰, the length of the arc is…

Answer 19

x/360(2πr)

Question 20

The area of the sector (of a circle) formed by the arc x⁰ and 2 radii is…

Answer 20

x/360(πr²)

Question 21

The dimensions of a box are l, w, and h. What is the length of its diagonal, d?

Answer 21

d = sqrt (l² + w² + h²)

Question 22

The volume of a cylinder is:

Answer 22

V = πr² * h

Question 23

The surface area of a cylinder is:

Answer 23

A = 2πr² + 2πrh

Question 24

The exterior angle of a triangle is equal to…

Answer 24

…the sum of the to remote interior angles.