Geometry Basics: Master the Fundamentals of Geometry

Question 1

Which of the following is NOT considered a basic geometric shape in Euclidean geometry?

Accepted Answer

Sphere

Answer

Point

Answer

Line

Answer

Triangle

Question 2

An angle measuring less than 90 degrees is classified as a/an:

Accepted Answer

Acute angle

Answer

Obtuse angle

Answer

Right angle

Answer

Straight angle

Question 3

A triangle with two equal sides is known as a/an:

Accepted Answer

Isosceles triangle

Answer

Equilateral triangle

Answer

Scalene triangle

Answer

Right triangle

Question 4

The Pythagorean theorem is primarily used to determine the length of the:

Accepted Answer

Hypotenuse in a right triangle

Answer

Base of a triangle

Answer

Height of a triangle

Answer

Area of a triangle

Question 5

A circle is defined as the set of points:

Accepted Answer

Equidistant from a fixed point

Answer

Lying on the same plane

Answer

Intersecting at a common point

Answer

Forming a square

Question 6

The formula for calculating the area of a circle is:

Accepted Answer

A = πr²

Answer

A = 4πr²

Answer

A = 2πr

Answer

A = πr

Question 7

A polyhedron with six square faces is called a:

Accepted Answer

Cube

Answer

Prism

Answer

Pyramid

Answer

Sphere

Question 8

Which of the following is NOT considered a basic geometric figure introduced in this unit?

Accepted Answer

Sphere

Answer

Point

Answer

Line

Answer

Triangle

Question 9

What is the formula used to calculate the area of a circle?

Accepted Answer

A = πr²

Answer

A = 2πr

Answer

A = 4πr²

Answer

A = πr

Question 10

What is the famous theorem used to relate the lengths of sides in a right triangle?

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

c² - a² = b²

Answer

b² + c² = a²

Question 11

What is the formula used to calculate the volume of a rectangular prism?

Accepted Answer

V = lwh

Answer

V = 2lw + 2lh + 2wh

Answer

V = πr²h

Answer

V = 4/3πr³

Question 12

What is the formula used to calculate the surface area of a sphere?

Accepted Answer

A = 4πr²

Answer

A = πr²

Answer

A = 2πr³

Answer

A = 4/3πr³

Question 13

What type of geometric figure is formed when a cone is intersected by a plane parallel to its base?

Accepted Answer

Circle

Answer

Ellipse

Answer

Triangle

Answer

Square

Question 14

In a circle, a straight line segment joining two points on the circle and passing through the center is known as a:

Accepted Answer

Diameter

Answer

Radius

Answer

Chord

Answer

Secant

Question 15

Which of the following angles measures less than 90 degrees?

Accepted Answer

30 degrees

Answer

90 degrees

Answer

120 degrees

Answer

180 degrees

Question 16

A polygon with four sides is called a:

Accepted Answer

Quadrilateral

Answer

Triangle

Answer

Pentagon

Answer

Hexagon

Question 17

The sum of the interior angles of a triangle measures:

Accepted Answer

180 degrees

Answer

90 degrees

Answer

120 degrees

Answer

270 degrees

Question 18

Identify the figure that is NOT a basic geometric figure:

Accepted Answer

Sphere

Answer

Point

Answer

Line

Answer

Triangle

Question 19

Determine the number of points that define a line:

Accepted Answer

2

Answer

1

Answer

3

Answer

4 or more

Question 20

Select the property that accurately describes a plane:

Accepted Answer

It extends infinitely in all directions and has no thickness.

Answer

It is a one-dimensional figure.

Answer

It has a defined perimeter.

Answer

It is a three-dimensional object.

Question 21

Identify the measure of an angle that forms a straight line:

Accepted Answer

180 degrees

Answer

30 degrees

Answer

90 degrees

Answer

270 degrees

Question 22

State the Pythagorean Theorem:

Accepted Answer

a^2 + b^2 = c^2

Answer

a^2 - b^2 = c^2

Answer

a^2 + b^2 = c

Answer

a^2 - b^2 = c

Question 23

Determine the formula for the area of a circle:

Accepted Answer

πr^2

Answer

2πr

Answer

4πr^2

Answer

πr

Question 24

Which of the following is NOT a fundamental element of geometry?

Accepted Answer

Cylinder

Answer

Point

Answer

Line

Answer

Plane

Question 25

What is the term for two lines that will never cross?

Accepted Answer

Parallel lines

Answer

Perpendicular lines

Answer

Intersecting lines

Answer

Transversal lines

Question 26

What is the measure of the angle formed by two perpendicular lines?

Accepted Answer

90 degrees

Answer

30 degrees

Answer

45 degrees

Answer

180 degrees

Question 27

What formula is used to calculate the area of a triangle?

Accepted Answer

A = ½ * base * height

Answer

A = base * height

Answer

A = π * r²

Answer

A = 4 * π * r²

Question 28

What is the primary purpose of the Pythagorean theorem?

Accepted Answer

Finding the length of the hypotenuse of a right triangle

Answer

Finding the area of a circle

Answer

Finding the volume of a sphere

Answer

Finding the surface area of a cube

Question 29

What is the total measure of the interior angles of a pentagon?

Accepted Answer

540 degrees

Answer

180 degrees

Answer

360 degrees

Answer

720 degrees

Question 30

How can you tell if two lines are perpendicular?

Accepted Answer

Check if they intersect to form four right angles (90 degrees).

Answer

Check if the lines are parallel.

Answer

Check if the lines have equal lengths.

Answer

Count how many points are on the lines.

Question 31

Which transformation flips a figure over a vertical line, creating a mirror image?

Accepted Answer

Reflection over the vertical axis

Answer

Rotation

Answer

Reflection over the horizontal axis

Answer

Translation

Question 32

Which of these is a straight path with two distinct endpoints?

Accepted Answer

Line

Answer

Plane

Answer

Ray

Answer

Triangle

Question 33

What is the sum of the interior angles of a triangle?

Accepted Answer

180 degrees

Answer

90 degrees

Answer

270 degrees

Answer

360 degrees

Question 34

Which of the following describes a line that intersects another line at a right angle?

Accepted Answer

Perpendicular

Answer

Parallel

Answer

Tangent

Answer

Intersecting

Question 35

What three-dimensional figure has six square sides?

Accepted Answer

Cube

Answer

Cylinder

Answer

Cone

Answer

Sphere

Question 36

Which of these figures is a four-sided polygon?

Accepted Answer

Square

Answer

Triangle

Answer

Circle

Answer

Sphere

Question 37

Which formula calculates the area of a triangle?

Accepted Answer

A = bh / 2

Answer

A = πr²

Answer

A = lw

Answer

A = 4πr²

Question 38

What two-dimensional shape is defined by three or more straight sides?

Accepted Answer

Polygon

Answer

Line

Answer

Angle

Answer

Circle

Question 39

Which characteristic defines a parallelogram?

Accepted Answer

Opposite sides are parallel

Answer

Equal sides

Answer

Adjacent sides are perpendicular

Answer

All angles are obtuse

Question 40

What is the name of the line segment from the center of a circle to a point on its circumference?

Accepted Answer

Radius

Answer

Diameter

Answer

Chord

Answer

Tangent

Question 41

Which of the following is NOT a basic geometric figure?

Accepted Answer

Sphere

Answer

Point

Answer

Line

Answer

Plane

Question 42

Which of the following is a two-dimensional figure?

Accepted Answer

Triangle

Answer

Cube

Answer

Cone

Answer

Sphere

Question 43

What is the measure of a right angle?

Accepted Answer

90 degrees

Answer

180 degrees

Answer

360 degrees

Answer

270 degrees

Question 44

Which of the following is a property of parallel lines?

Accepted Answer

They never intersect.

Answer

They always intersect.

Answer

They intersect at a right angle.

Answer

They intersect at an acute angle.

Question 45

What is the formula for finding the area of a trapezoid?

Accepted Answer

1/2 * (b1 + b2) * h

Answer

b * h

Answer

1/2 * b * h

Answer

(b1 + b2) * h

Question 46

Which of the following is a type of triangle that has at least two equal sides?

Accepted Answer

Isosceles triangle

Answer

Scalene triangle

Answer

Right triangle

Answer

Equilateral triangle

Question 47

Which of the following is a type of transformation that moves a figure from one location to another without changing its size or shape?

Accepted Answer

Translation

Answer

Reflection

Answer

Rotation

Question 48

What is the formula used to find the area of a circle?

Accepted Answer

πr²

Answer

2πr

Answer

4πr