Plane Geometry Quizzes: Test Your Knowledge of Flat Surface Geometry

Question 1

Given a circle of radius r, what formula represents its circumference?

Accepted Answer

2πr

Answer

πr^2

Answer

4πr

Answer

πr

Question 2

Which of the following angle measures cannot be an interior angle of a triangle?

Accepted Answer

185°

Answer

30°

Answer

90°

Answer

120°

Question 3

If two lines intersect and create four congruent angles, what are those angles classified as?

Accepted Answer

Supplementary

Answer

Complementary

Answer

Right

Answer

Obtuse

Question 4

Which transformation below does NOT preserve the area of a figure?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 5

Given a regular hexagon, what is the measure of one of its exterior angles?

Accepted Answer

60°

Answer

30°

Answer

90°

Answer

120°

Question 6

Which of the provided sets of numbers does NOT form a Pythagorean triple?

Accepted Answer

(6, 8, 10)

Answer

(3, 4, 5)

Answer

(5, 12, 13)

Answer

(8, 15, 17)

Question 7

What is the slope of a line that is parallel to the x-axis?

Accepted Answer

0

Answer

1

Answer

Undefined

Answer

Varies

Question 8

Which theorem allows us to determine the area of a triangle using its base and height?

Accepted Answer

Area of Triangle Theorem

Answer

Pythagorean Theorem

Answer

Triangle Inequality Theorem

Answer

Law of Cosines

Question 9

What formula calculates the volume of a cone with radius 'r' and height 'h'?

Accepted Answer

1/3πr^2h

Answer

πr^2h

Answer

2πr^2h

Answer

πr^3h

Question 10

The Pythagorean Theorem is primarily used to find the length of which part of a right triangle?

Accepted Answer

Hypotenuse

Answer

Leg

Answer

Altitude

Answer

Median

Question 11

Which condition is necessary for two triangles to be congruent by the SAS congruence theorem?

Accepted Answer

Two sides and the included angle are congruent.

Answer

Two angles and the included side are congruent.

Answer

Two angles and a non-included side are congruent.

Answer

Three sides are congruent.

Question 12

Which of the following is not a criterion for the similarity of triangles?

Accepted Answer

Equal perimeters.

Answer

Corresponding angles are congruent.

Answer

Corresponding sides are proportional.

Answer

Identical shapes but potentially different sizes.

Question 13

Which theorem is associated with circles?

Accepted Answer

Circle Secant Theorem

Answer

Pythagorean Theorem

Answer

Triangle Sum Theorem

Answer

Angle Bisector Theorem

Question 14

Write the equation of a circle with a radius of 3 and a center at the origin.

Accepted Answer

x² + y² = 9

Answer

x² - y² = 9

Answer

y² - x² = 9

Answer

x² + 2y² = 9

Question 15

The transformation that rotates a shape around a fixed point is:

Accepted Answer

Rotation

Answer

Translation

Answer

Reflection

Answer

Dilation

Question 16

According to the Pythagorean theorem, the sum of the squares of the lengths of the two shorter sides (legs) of a right triangle is equal to:

Accepted Answer

The square of the longest side (hypotenuse)

Answer

The square of the sum of the lengths of the legs

Answer

The square of the difference of the lengths of the legs

Answer

The square of the product of the lengths of the legs

Question 17

A quadrilateral with one pair of parallel sides is known as a:

Accepted Answer

Trapezoid

Answer

Square

Answer

Parallelogram

Answer

Rhombus

Question 18

The area of the surface covering a sphere is referred to as its:

Accepted Answer

Surface area

Answer

Volume

Answer

Circumference

Answer

Radius

Question 19

Which condition is essential for two triangles to be congruent under the Side-Side-Side (SSS) congruence rule?

Accepted Answer

All pairs of corresponding sides must be equal in length.

Answer

All pairs of corresponding angles must be equal in measure.

Answer

All pairs of corresponding altitudes must be equal in length.

Answer

All pairs of corresponding medians must be equal in length.

Question 20

Which statement accurately describes the diagonals of a parallelogram?

Accepted Answer

The diagonals are congruent and bisect each other.

Answer

The diagonals are perpendicular to each other.

Answer

The diagonals are parallel to each other.

Answer

The diagonals are equal in length but do not bisect each other.

Question 21

What is the volume of a sphere with a diameter of 12 units?

Accepted Answer

(48π/3)

Answer

(12π/3)

Answer

(24π/3)

Answer

(96π/3)

Question 22

Which transformation preserves both distance and angle measure?

Accepted Answer

Rotation

Answer

Scaling

Answer

Translation

Answer

Shear

Question 23

**Properties of a Square**
Which of the following accurately describes the properties of a square?

Accepted Answer

Four equal sides and four right angles

Answer

No equal sides and no right angles

Answer

Two pairs of parallel sides and two right angles

Answer

Three equal sides and three right angles

Question 24

**Regular Polygon Property**
Which statement accurately describes a property of a regular polygon?

Accepted Answer

All sides and angles are equal

Answer

All angles are equal, but not all sides

Answer

Neither all sides nor all angles are equal

Answer

All sides are equal, but not all angles

Question 25

**Parallel Line Equation**
Write the equation of a line that is parallel to the x-axis and passes through the point (2, -5):

Accepted Answer

y = -5

Answer

x = -5

Answer

y = 2

Question 26

Find the sum of the interior angles of a regular pentagon.

Accepted Answer

540 degrees

Answer

720 degrees

Answer

360 degrees

Answer

900 degrees

Question 27

Which of the following is a classification of a triangle based on its side lengths?

Accepted Answer

Equilateral triangle

Answer

Right triangle

Answer

Isosceles triangle

Answer

Congruent triangle

Question 28

Identify the term used to describe two angles that sum up to 90 degrees.

Accepted Answer

Complementary angles

Answer

Supplementary angles

Answer

Adjacent angles

Answer

Vertical angles

Question 29

State the formula for calculating the area of a circle.

Accepted Answer

πr²

Answer

2πr

Answer

πd

Answer

4πr²

Question 30

When the diagonal of a square divides it, what type of triangles are formed?

Accepted Answer

Congruent right triangles

Answer

Equilateral triangles

Answer

Isosceles triangles

Answer

Similar right triangles

Question 31

What conditions must be met for two triangles to be considered similar?

Accepted Answer

Corresponding angles congruent and corresponding sides proportional

Answer

Only corresponding angles congruent

Answer

All sides congruent

Question 32

Find the circumference of a circle with a radius of 5 cm.

Accepted Answer

10π cm

Answer

25π cm

Answer

20π cm

Answer

5π cm

Question 33

What is the name of a polygon with all sides and angles equal?

Accepted Answer

Regular polygon

Answer

Irregular polygon

Answer

Concave polygon

Answer

Convex polygon

Question 34

What is the name of a triangle with three equal sides?

Accepted Answer

Equilateral triangle

Answer

Isosceles triangle

Answer

Scalene triangle

Question 35

Determine the sum of the interior angles of a quadrilateral.

Accepted Answer

360 degrees

Answer

540 degrees

Answer

180 degrees

Answer

720 degrees

Question 36

The area of a rectangle with a length of 8 cm and a width of 5 cm is:

Accepted Answer

40 cm²

Answer

13 cm²

Answer

26 cm²

Answer

64 cm²

Question 37

A triangle with two equal sides and two equal angles is called a(n):

Accepted Answer

Isosceles triangle

Answer

Equilateral triangle

Answer

Scalene triangle

Question 38

The diagonal of a square with side length 's' is:

Accepted Answer

√2s

Answer

s²

Answer

2s

Answer

s√3

Question 39

Two angles are supplementary if their sum is:

Accepted Answer

180 degrees

Answer

90 degrees

Answer

360 degrees

Question 40

A parallelogram with all four sides equal is called a:

Accepted Answer

Rhombus

Answer

Trapezoid

Answer

Square

Answer

Rectangle

Question 41

The area of a triangle with a base of 12 cm and a height of 8 cm is:

Accepted Answer

48 cm²

Answer

96 cm²

Answer

120 cm²

Answer

24 cm²

Question 42

In a right-angled triangle, the side opposite the right angle is called the:

Accepted Answer

Hypotenuse

Answer

Median

Answer

Base

Answer

Altitude