Plane Geometry Quizzes: Test Your Geometric Skills

Question 1

A triangle has side lengths of 5 cm, 12 cm, and 13 cm. What is the type of triangle?

Accepted Answer

Right-angled

Answer

Acute

Answer

Obtuse

Answer

Isosceles

Question 2

If two sides of a quadrilateral are parallel while the other two sides are not, what type of quadrilateral is it?

Accepted Answer

Trapezoid

Answer

Parallelogram

Answer

Rectangle

Answer

Rhombus

Question 3

In a circle, the radius drawn to a chord perpendicularly:

Accepted Answer

Divides the chord into two equal parts

Answer

Divides the chord in the golden ratio

Answer

Is the longest chord

Answer

Is the shortest chord

Question 4

Which of the following is not an example of a cyclic quadrilateral?

Accepted Answer

Trapezoid

Answer

Square

Answer

Rhombus

Answer

Parallelogram

Question 5

Which of the following transformations does NOT preserve the shape of a figure?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 6

What is the gradient of a line parallel to a line with gradient 3?

Accepted Answer

3

Answer

1/3

Answer

-3

Answer

-1/3

Question 7

Which property guarantees that two triangles are congruent?

Accepted Answer

Equal side lengths and equal angles

Answer

Equal area and equal perimeter

Answer

Similar angles and proportional side lengths

Question 8

In a quadrilateral, which pair of angles are always complementary?

Accepted Answer

Opposite angles

Answer

Adjacent angles

Answer

Alternate angles

Question 9

A square has a side length of 10 cm. What is the radius of the largest circle that can be inscribed in it?

Accepted Answer

5 cm

Answer

10 cm

Answer

15 cm

Question 10

Which of the following statements about similar triangles is true?

Accepted Answer

Areas are proportional to the squares of the corresponding sides

Answer

Corresponding altitudes are equal

Answer

Ratios of corresponding medians are equal

Question 11

Which of the following transformations can change the size of a figure?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 12

In a parallelogram, the diagonals always intersect at a right angle.

Accepted Answer

True

Answer

False

Question 13

Which of the following is NOT a property of a cyclic quadrilateral?

Accepted Answer

Perimeter is always divisible by 4

Answer

Opposite angles are supplementary

Answer

Diagonals bisect each other

Question 14

In a triangle, the sum of the interior angles is always equal to:

Accepted Answer

180 degrees

Answer

90 degrees

Answer

120 degrees

Answer

270 degrees

Question 15

If two triangles have the same shape and size, they are said to be:

Accepted Answer

Congruent

Answer

Similar

Answer

Isometric

Answer

Equivalent

Question 16

The circumference of a circle with radius 'r' is:

Accepted Answer

2πr

Answer

πr

Answer

πr^2

Answer

2πr^2

Question 17

Two circles are tangent to each other if they:

Accepted Answer

Have one point in common

Answer

Have no points in common

Answer

Have two points in common

Answer

Have three points in common

Question 18

If two triangles have the same angles but different side lengths, they are said to be:

Accepted Answer

Similar

Answer

Congruent

Answer

Equivalent

Answer

Isometric

Question 19

Which of the following is a regular polygon?

Accepted Answer

Square

Answer

Rectangle

Answer

Trapezoid

Answer

Parallelogram

Question 20

Which of the following is a defining property of congruent triangles?

Accepted Answer

Equal side lengths and equal angles

Answer

Equal side lengths and equal areas

Answer

Equal angles and equal areas

Answer

Equal areas and equal volumes

Question 21

Which of the following is a necessary condition for two triangles to be congruent by the SSS congruence theorem?

Accepted Answer

All three pairs of corresponding sides are equal.

Answer

All three pairs of corresponding angles are equal.

Answer

The areas of the triangles are equal.

Answer

The perimeters of the triangles are equal.

Question 22

Given a triangle with sides of length a, b, and c, what is the formula for its area?

Accepted Answer

√(s(s - a)(s - b)(s - c))

Answer

as/2

Answer

ab/2

Answer

(a + b + c)/2

Question 23

In a regular hexagon, what is the measure of each interior angle?

Accepted Answer

120 degrees

Answer

60 degrees

Answer

90 degrees

Answer

180 degrees

Question 24

What is the sum of the interior angles in a quadrilateral?

Accepted Answer

360 degrees

Answer

180 degrees

Answer

540 degrees

Answer

720 degrees

Question 25

For two triangles to be congruent by the SAS (Side-Angle-Side) theorem, which condition must be met?

Accepted Answer

Two sides and the included angle are equal.

Answer

Two angles and the included side are equal.

Answer

Three sides are equal.

Answer

Three angles are equal.

Question 26

In a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This statement is known as:

Accepted Answer

Pythagoras' theorem

Answer

Euclid's theorem

Answer

Euler's theorem

Answer

Descartes' theorem

Question 27

Which of the following is NOT a property of a circle?

Accepted Answer

A circle can be drawn inside a square

Answer

All points on the circle are the same distance from the center

Answer

The diameter of a circle is twice its radius

Answer

A circle has no corners

Question 28

The total of the interior angles of a quadrilateral is:

Accepted Answer

360 degrees

Answer

180 degrees

Answer

540 degrees

Answer

720 degrees

Question 29

Two triangles are congruent if:

Accepted Answer

Their corresponding sides and angles are equal

Answer

Their corresponding angles are equal

Answer

Their corresponding sides are equal

Answer

Their areas are equal

Question 30

The area of a triangle can be calculated using the formula:

Accepted Answer

1/2 * base * height

Answer

base * height

Answer

π * radius^2

Answer

4/3 * π * radius^3

Question 31

Find the perimeter of a rectangle with a length of 5 cm and a width of 3 cm:

Accepted Answer

16 cm

Answer

8 cm

Answer

30 cm

Answer

60 cm

Question 32

Calculate the circumference of a circle with a radius of 6 cm:

Accepted Answer

12π cm

Answer

6π cm

Answer

36π cm

Answer

72π cm

Question 33

The diagonals of a rhombus are perpendicular and bisect each other. Is this statement true or false?

Accepted Answer

True

Answer

False

Question 34

In a triangle with side lengths of 5 cm, 12 cm, and 13 cm, which angle is the largest?

Accepted Answer

Angle opposite to the longest side of 13 cm

Answer

All angles are equal

Answer

Angle opposite to the middle side of 12 cm

Answer

Angle opposite to the shortest side of 5 cm

Question 35

Which of the following transformations preserves both length and angle measures?

Accepted Answer

Rigid transformation

Answer

Translation

Answer

Reflection

Answer

Dilation

Question 36

If two triangles have the same base and height, their areas are in the ratio of:

Accepted Answer

1:1

Answer

1:2

Answer

1:4

Answer

2:1

Question 37

In a triangle with sides of length 5, 7, and 9, which side is opposite the largest angle?

Accepted Answer

9

Answer

7

Answer

5

Answer

Cannot be determined from the provided information

Question 38

A quadrilateral with two pairs of parallel sides is called a:

Accepted Answer

Parallelogram

Answer

Rhombus

Answer

Kite

Answer

Trapezoid

Question 39

Two triangles are congruent by the SAS (Side-Angle-Side) congruence rule if:

Accepted Answer

Two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle.

Answer

Two sides and an angle not included between them of one triangle are congruent to two sides and an angle not included between them of the other triangle.

Answer

All three pairs of corresponding sides are congruent.

Answer

Two angles and a side of one triangle are congruent to two angles and a side of the other triangle.

Question 40

According to the Pythagorean Theorem, in a right-angled triangle, the square of the hypotenuse is equal to:

Accepted Answer

The sum of the squares of the other two sides.

Answer

The product of the other two sides.

Answer

The square root of the sum of the squares of the other two sides.

Question 41

Two triangles are similar if:

Accepted Answer

Their corresponding angles are congruent and their corresponding sides are proportional.

Answer

Their corresponding sides and angles are congruent.

Answer

Their corresponding sides are congruent and their corresponding angles are proportional.

Question 42

The circumcircle of a triangle is a circle that:

Accepted Answer

Passes through all three vertices of the triangle.

Answer

Is tangent to all three sides of the triangle.

Answer

Is inscribed within the triangle.

Question 43

The centroid of a triangle is the point where the:

Accepted Answer

Medians intersect.

Answer

Altitudes intersect.

Answer

Perpendicular bisectors intersect.

Answer

Angle bisectors intersect.

Question 44

Two triangles are similar if their corresponding angles are equal and their corresponding sides are  _________ .

Accepted Answer

proportional

Answer

parallel

Answer

congruent

Answer

perpendicular

Question 45

The sum of the interior angles of any triangle is always equal to:

Accepted Answer

180 degrees

Answer

360 degrees

Answer

270 degrees

Answer

90 degrees

Question 46

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

Accepted Answer

Square

Answer

Rectangle

Answer

Rhombus

Answer

Trapezium

Question 47

The area of a triangle is calculated using the formula:

Accepted Answer

(1/2) * base * height

Answer

base * height

Answer

π * radius²

Answer

length * width

Question 48

If the circumference of a circle is 12π, what is the radius of the circle?

Accepted Answer

6

Answer

3

Answer

12

Answer

24

Question 49

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

Accepted Answer

hypotenuse

Answer

base

Answer

altitude

Answer

perpendicular

Question 50

The diameter of a circle is twice the length of its:

Accepted Answer

radius

Answer

chord

Answer

arc

Answer

circumference

Question 51

Two triangles are congruent if they have the same shape and  _________ .

Accepted Answer

size

Answer

orientation

Answer

texture

Answer

color

Question 52

What is the formula for calculating the area of a circle?

Accepted Answer

π * radius²

Answer

π * diameter²

Answer

π * radius

Answer

2 * π * radius

Question 53

What is the ratio of a circle's circumference to its diameter?

Accepted Answer

π

Answer

1

Answer

2π

Answer

π/2