Plane Geometry Quizzes: Master Geometry Concepts

Question 1

Which condition is not essential for triangle congruence?

Accepted Answer

Two pairs of corresponding altitudes are congruent

Answer

Two pairs of corresponding sides are congruent

Answer

Two pairs of corresponding angles are congruent

Answer

The third pair of corresponding parts are congruent

Question 2

In the equation of a circle, (x - h)² + (y - k)² = r², which term represents the center of the circle?

Accepted Answer

(h, k)

Answer

(r, h)

Answer

(h, r)

Answer

(k, r)

Question 3

Which angle theorem states that the exterior angle of a triangle is equal to the sum of the opposite interior angles?

Accepted Answer

Exterior Angle Theorem

Answer

Angle Sum Theorem

Answer

Triangle Inequality Theorem

Answer

Pythagorean Theorem

Question 4

Calculate the distance between the points (2, 3) and (-1, 5).

Accepted Answer

2√10

Answer

2

Answer

4

Answer

√10

Question 5

If two triangles are similar, the ratio of their corresponding sides is:

Accepted Answer

Proportional

Answer

Equal

Answer

Inversely proportional

Answer

Independent

Question 6

Which of the following is the correct trigonometric ratio for finding the length of the hypotenuse in a right-angled triangle?

Accepted Answer

cos θ = adjacent/hypotenuse

Answer

sin θ = opposite/hypotenuse

Answer

tan θ = opposite/adjacent

Answer

cot θ = adjacent/opposite

Question 7

Which theorem establishes the relationship between the areas of similar triangles?

Accepted Answer

Triangle Similarity Theorem

Answer

Pythagorean Theorem

Answer

Converse of Triangle Inequality Theorem

Answer

Law of Cosines

Question 8

Classify the triangle with side lengths AB = 6 cm, AC = 8 cm, and BC = 10 cm.

Accepted Answer

Scalene

Answer

Isosceles

Answer

Right-angled

Answer

Equilateral

Question 9

Select the correct formula for the volume of a sphere with radius r:

Accepted Answer

4/3πr³

Answer

πr³

Answer

2/3πr³

Answer

1/3πr³

Question 10

Identify the midpoint formula for the line segment connecting points (x₁, y₁) and (x₂, y₂).

Accepted Answer

((x₁ + x₂)/2, (y₁ + y₂)/2)

Answer

((x₁ - x₂)/2, (y₁ - y₂)/2)

Answer

((x₁ × x₂)/2, (y₁ × y₂)/2)

Answer

(x₁ + x₂, y₁ + y₂)

Question 11

The area of a circle has a direct proportional relationship with the square of its:

Accepted Answer

Radius

Answer

Diameter

Answer

Circumference

Answer

Height

Question 12

Which transformation does NOT preserve congruence?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 13

Which of the following is NOT a trigonometric function?

Accepted Answer

Exponential

Answer

Sine

Answer

Cosine

Answer

Tangent

Question 14

In a 30-60-90 degree triangle, the ratio of the length of the shortest side to the length of the longest side is:

Accepted Answer

1 : √2 : 2

Answer

1 : 2 : √3

Answer

√2 : 1 : √3

Answer

√3 : 2 : 1

Question 15

In an isosceles triangle, which property holds true?

Accepted Answer

Only two sides are equal in length.

Answer

All three sides are equal in length.

Answer

Base angles are always congruent.

Answer

Sum of base angles is always 90°.

Question 16

Calculate the length of the hypotenuse of a right triangle with legs measuring 5 cm and 12 cm.

Accepted Answer

17 cm

Answer

7 cm

Answer

13 cm

Answer

25 cm

Question 17

Find the radius of a circle with a diameter of 10 cm.

Accepted Answer

5 cm

Answer

2.5 cm

Answer

12.5 cm

Answer

20 cm

Question 18

Calculate the area of a triangle with a base of 8 cm and a height of 12 cm.

Accepted Answer

48 sq cm

Answer

24 sq cm

Answer

72 sq cm

Answer

96 sq cm

Question 19

Which statement accurately describes congruent triangles?

Accepted Answer

Identical in shape and size

Answer

Identical in perimeter

Answer

Identical in area

Answer

Mirror images of each other

Question 20

Which of the following statements about triangles is always true?

Accepted Answer

The sum of the interior angles of a triangle is 180 degrees.

Answer

All triangles have three equal sides.

Answer

An equilateral triangle is also an isosceles triangle.

Answer

A scalene triangle has two equal angles.

Question 21

Which of the following quadrilaterals has four equal sides and four right angles?

Accepted Answer

Rectangle

Answer

Parallelogram

Answer

Rhombus

Answer

Trapezium

Question 22

Which of the following transformations does not preserve distance?

Accepted Answer

Shear

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 23

What is the slope of the line passing through the points (x1, y1) and (x2, y2)?

Accepted Answer

(y2 - y1) / (x2 - x1)

Answer

(x2 - x1) / (y2 - y1)

Answer

(y1 - y2) / (x1 - x2)

Answer

(x1 - x2) / (y1 - y2)

Question 24

Which of the following is a similarity transformation that increases the size of a figure?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 25

What is the area of a triangle with base b and height h?

Accepted Answer

1/2 * b * h

Answer

b * h

Answer

1/2 * h * b

Answer

2 * b * h

Question 26

Which of the following is the Pythagorean Theorem?

Accepted Answer

a² + b² = c²

Answer

a² + c² = b²

Answer

b² + c² = a²

Answer

a² - b² = c²

Question 27

What is the length of the hypotenuse of a right triangle with legs of length a and b?

Accepted Answer

√(a² + b²)

Answer

a² + b²

Answer

a - b

Answer

a * b

Question 28

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

Accepted Answer

Adjacent sides are perpendicular

Answer

Opposite sides are parallel

Answer

Opposite sides are congruent

Answer

Diagonals bisect each other

Question 29

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

Accepted Answer

25π cm²

Answer

50π cm²

Question 30

Determine the equation of the line passing through the points (2, 3) and (-1, 5).

Accepted Answer

y = -x + 7

Answer

y = 2x + 1

Question 31

Find the perimeter of a square with a side length of 8 cm.

Accepted Answer

32 cm

Question 32

Which of the following is NOT a trigonometric ratio?

Accepted Answer

Perimeter

Answer

Sine

Answer

Cosine

Question 33

Find the distance between the points (3, 4) and (-1, 2) using the distance formula.

Accepted Answer

4√5 units

Question 34

In a right-angled triangle, which side is opposite the right angle?

Accepted Answer

Opposite

Question 35

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

Accepted Answer

Opposite sides are congruent but not parallel

Answer

All sides are equal in length

Answer

Opposite angles are equal in measure

Answer

Diagonals intersect at right angles

Question 36

Find the equation of the circle having its center at (2, -3) and a radius of 5 units.

Accepted Answer

(x - 2)² + (y + 3)² = 25

Answer

(x - 2)² - (y + 3)² = 25

Answer

25 = (x + 2)² + (y - 3)²

Answer

25 = (x - 2)² - (y + 3)²

Question 37

In a parallelogram, do the diagonals always bisect each other?

Accepted Answer

Yes

Answer

No

Question 38

Which of the following is a condition for congruence of triangles by the Side-Angle-Side (SAS) property?

Accepted Answer

Two sides and the included angle are congruent

Answer

Two sides and the non-included angle are congruent

Answer

Two angles and the included side are congruent

Answer

Two angles and the non-included side are congruent

Question 39

In a circle with radius r, what is the formula for the area of a sector with central angle θ?

Accepted Answer

(1/2)πr²θ

Answer

πr²θ

Answer

2πrθ

Answer

(1/2)πrθ

Question 40

Which theorem states that the sum of the interior angles of a triangle is 180°?

Accepted Answer

Triangle Sum Theorem

Answer

Pythagorean Theorem

Answer

Converse of the Pythagorean Theorem

Answer

Angle Bisector Theorem

Question 41

What condition must be met for two lines to be parallel?

Accepted Answer

They have the same slope.

Answer

They have the same y-intercept.

Answer

They intersect at a right angle.

Answer

They have different slopes.

Question 42

In a triangle, the sum of the interior angles is what value in degrees?

Accepted Answer

180

Answer

120

Answer

270

Answer

360

Question 43

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

Accepted Answer

All sides are congruent

Answer

Opposite sides are parallel and of equal length

Answer

Opposite angles are equal

Answer

Diagonals bisect each other

Question 44

Two triangles are similar if:

Accepted Answer

Their corresponding sides are in proportion

Answer

They have the same shape but not necessarily the same size

Answer

They have the same angles but not necessarily the same sides

Answer

They have the same perimeter

Question 45

What are the coordinates of the midpoint of the line segment joining the points (2, 3) and (6, 9)?

Accepted Answer

(4, 6)

Answer

(3, 5)

Answer

(5, 7)

Answer

(6, 8)

Question 46

Which of the following transformations is NOT a rigid motion?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 47

True or False: The diagonals of a rhombus are perpendicular to each other.

Accepted Answer

True

Answer

False

Question 48

To which type of triangle does the Pythagorean theorem apply?

Accepted Answer

Right-angled triangles

Answer

Isosceles triangles

Answer

Equilateral triangles

Answer

All triangles

Question 49

In a right-angled triangle, the ratio of the length of the opposite side to the length of the hypotenuse is known as:

Accepted Answer

Sine

Answer

Cosecant

Answer

Tangent

Answer

Cosine

Question 50

Which of the following properties does NOT apply to a parallelogram?

Accepted Answer

Diagonals perpendicularly bisect each other

Answer

Adjacent sides are equal

Answer

Opposite sides are parallel

Answer

Opposite angles are congruent

Question 51

The formula for calculating the area of a circle with a radius 'r' is:

Accepted Answer

πr²

Answer

2πr²

Answer

2πr

Answer

πr

Question 52

Which transformation preserves both the shape and size of a figure?

Accepted Answer

Translation

Answer

Reflection

Answer

Enlargement

Answer

Rotation

Question 53

Two triangles are similar if they have:

Accepted Answer

Proportional side lengths and congruent angles

Answer

Equivalent perimeters and areas

Answer

Equal areas and perimeters

Answer

Identical side lengths and angles

Question 54

The equation of a straight line with gradient 'm' and y-intercept 'b' is expressed as:

Accepted Answer

y = mx + b

Answer

y = cx + m

Answer

x = cx + m

Answer

x = my + c

Question 55

The area of a triangle with base length 'b' and height 'h' is calculated as:

Accepted Answer

½bh

Answer

bh

Answer

2bh

Answer

¼bh