Geometry for Year 10: Master Shapes and their Properties

Question 1

Question:

What is symmetry in geometry? Describe the different types of symmetry, such as line symmetry and rotational symmetry, and provide examples of symmetrical shapes.

Accepted Answer

A symmetrical shape has one or more lines of symmetry that divide the shape into two identical halves.

Accepted Answer

Rotational symmetry refers to the number of times a shape can be rotated around a point to match its original position.

Answer

Symmetry refers to the balance of shapes and sizes of different geometric figures.

Answer

Symmetrical shapes always have the same area and perimeter.

Question 2

Question:

What are similarity ratios, and how are they used in geometry? Give an example to show how similarity ratios help solve problems involving similar shapes.

Accepted Answer

Similarity ratios compare the corresponding sides of similar shapes.

Answer

Similarity ratios compare the corresponding angles of similar shapes.

Answer

Similarity ratios are used to find the area of similar shapes.

Answer

Similarity ratios are used to find the volume of similar shapes.

Question 3

Which transformation will not change the size or shape of a figure?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 4

Which of the following is a regular polygon?

Accepted Answer

A square

Answer

A rectangle

Answer

A trapezoid

Answer

A parallelogram

Question 5

What is the measure of an angle that is complementary to a 30-degree angle?

Accepted Answer

90 degrees

Answer

30 degrees

Answer

60 degrees

Answer

120 degrees

Question 6

Calculate the volume of a cylinder with a radius of 3 cm and a height of 5 cm.

Accepted Answer

25π cm³

Answer

15π cm³

Answer

45π cm³

Answer

90π cm³

Question 7

What is the equation of a circle with center (-1, 3) and radius 4?

Accepted Answer

(x + 1)² + (y - 3)² = 16

Answer

(x - 1)² + (y + 3)² = 16

Answer

(x + 1)² + (y - 3)² = 4

Answer

(x - 1)² + (y + 3)² = 4

Question 8

Which of the following is a concave polygon?

Accepted Answer

Horseshoe shape

Answer

Triangle

Answer

Square

Answer

Pentagon

Question 9

Which of the following is a theorem that relates the lengths of the sides of a right-angled triangle?

Accepted Answer

Pythagorean Theorem

Answer

Sine Theorem

Answer

Cosine Theorem

Answer

Triangle Inequality Theorem

Question 10

What is the perimeter of a square with 5 cm sides?

Accepted Answer

20 cm

Answer

10 cm

Answer

25 cm

Answer

40 cm

Question 11

In a triangle, what is the sum of its interior angles?

Accepted Answer

180°

Answer

90°

Answer

270°

Answer

360°

Question 12

What is the area of a triangle with a base of 5 cm and a height of 3 cm?

Accepted Answer

8 cm²

Answer

6 cm²

Answer

10 cm²

Answer

15 cm²

Question 13

Which shape is a regular polygon?

Accepted Answer

Square

Answer

Rectangle

Answer

Trapezoid

Answer

Parallelogram

Question 14

State the Pythagorean theorem.

Accepted Answer

a^2 + b^2 = c^2

Answer

a^2 - b^2 = c^2

Answer

c^2 + b^2 = a^2

Answer

c^2 - a^2 = b^2

Question 15

Which transformation maintains the original figure's size and shape?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 16

Identify the regular polygon among the following:

Accepted Answer

Square

Answer

Rectangle

Answer

Rhombus

Answer

Trapezoid

Question 17

Find the measure of an angle that is supplementary to an angle of 110 degrees.

Accepted Answer

170 degrees

Answer

50 degrees

Answer

70 degrees

Answer

110 degrees

Question 18

Which of these is NOT a defining property of a circle?

Accepted Answer

It has two parallel tangents

Answer

All points on the circumference are equidistant from the center

Answer

Its perimeter is known as its circumference

Answer

It exhibits rotational symmetry

Question 19

If a triangle has two sides of equal length, it is classified as:

Accepted Answer

Isosceles

Answer

Equilateral

Answer

Scalene

Answer

Right-angled

Question 20

Which 3D shape has a circular base, a vertex directly above the center of the base, and a curved surface?

Accepted Answer

Cone

Answer

Cylinder

Answer

Sphere

Answer

Pyramid

Question 21

Which transformation maintains distance?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 22

Calculate the volume of a cone with radius 5 cm and height 10 cm:

Accepted Answer

50π cm³

Answer

25π cm³

Answer

100π cm³

Answer

200π cm³

Question 23

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

Accepted Answer

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

Answer

Two angles and one side of one triangle are equal to the corresponding two angles and side of the other triangle.

Answer

All three sides of one triangle are equal to the corresponding three sides of the other triangle.

Question 24

A cube has a side length of 4 cm. Calculate its volume and surface area. Include the units of measurement in your answer.

Accepted Answer

Volume: 64 cm³, Surface Area: 96 cm²

Answer

Volume: 16 cm³, Surface Area: 16 cm²

Answer

Volume: 16 cm³, Surface Area: 96 cm²

Answer

Volume: 64 cm³, Surface Area: 16 cm²

Question 25

Which shape is not a conic section?

Accepted Answer

Rectangle

Answer

Circle

Answer

Ellipse

Answer

Hyperbola

Question 26

What is a geometric locus? Provide examples and explain how it can be used to solve geometry problems.

Accepted Answer

A geometric locus is a set of points that meet a specific condition.

Answer

A geometric locus is a single point that meets a specific condition.

Answer

A geometric locus is a line that connects two points.

Answer

A geometric locus is a circle that is centered at a specific point.

Question 27

Which of the following is not a characteristic of a circle?

Accepted Answer

Equal side lengths

Answer

Equal radii from the center to every point on the circumference

Answer

Constant ratio of circumference to diameter

Answer

Central angle theorem applies

Question 28

Which type of angle measures between 90 and 180 degrees?

Accepted Answer

Obtuse

Answer

Acute

Answer

Right

Answer

Reflex

Question 29

State the formula for finding the circumference of a circle with radius r:

Accepted Answer

2πr

Answer

πr

Answer

πr²

Answer

4πr²

Question 30

Find the measure of an angle that is supplementary to an angle measuring 120 degrees:

Accepted Answer

180 degrees

Answer

30 degrees

Answer

60 degrees

Answer

120 degrees

Question 31

Which of the following is **not** a rigid transformation?

Accepted Answer

Dilation

Answer

Rotation

Answer

Reflection

Answer

Translation

Question 32

A two-dimensional shape with four equal sides and four right angles is a:

Accepted Answer

Square

Answer

Rectangle

Answer

Triangle

Answer

Circle

Question 33

The sum of the interior angles of a triangle amounts to:

Accepted Answer

180 degrees

Answer

360 degrees

Answer

270 degrees

Answer

90 degrees

Question 34

Which theorem relates the side lengths in a right-angled triangle?

Accepted Answer

Pythagoras' theorem

Answer

Triangle inequality

Answer

Cosine rule

Answer

Sine rule

Question 35

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

Accepted Answer

180 degrees

Answer

90 degrees

Answer

360 degrees

Answer

270 degrees

Question 36

Which shape has four equal sides and four right angles?

Accepted Answer

Square

Answer

Rhombus

Answer

Trapezoid

Answer

Rectangle

Question 37

A circle with a radius of 5 cm has an area of:

Accepted Answer

25π cm²

Answer

50π cm²

Answer

12.5π cm²

Answer

10π cm²

Question 38

What is the volume of a cube with sides of 4 cm each?

Accepted Answer

64 cm³

Answer

16 cm³

Answer

24 cm³

Answer

36 cm³

Question 39

The equation of a circle with center (2, 3) and radius 4 is:

Accepted Answer

(x - 2)² + (y - 3)² = 16

Answer

(x + 2)² + (y + 3)² = 16

Answer

(x + 2)² + (y - 3)² = 16

Answer

(x - 2)² + (y + 3)² = 16

Question 40

A triangle with all sides equal in length is called a(n):

Accepted Answer

Equilateral triangle

Answer

Scalene triangle

Answer

Isosceles triangle

Answer

Right-angled triangle

Question 41

The sum of the interior angles of a quadrilateral is:

Accepted Answer

360 degrees

Answer

180 degrees

Answer

270 degrees

Answer

540 degrees

Question 42

A circle with a radius of 5 cm has a circumference of:

Accepted Answer

10π cm

Answer

25π cm

Answer

5π cm

Question 43

A triangle with one angle measuring 90 degrees is called a(n):

Accepted Answer

Right-angled triangle

Answer

Equilateral triangle

Answer

Acute triangle

Answer

Obtuse triangle

Question 44

Which geometric transformation creates a mirror image of a shape?

Accepted Answer

Reflection

Answer

Enlargement

Answer

Translation

Answer

Rotation

Question 45

A regular hexagon has how many lines of symmetry?

Accepted Answer

6

Answer

4

Answer

3

Answer

8

Question 46

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

Accepted Answer

(1/2) * base * height

Answer

length * width

Answer

base * height

Answer

π * radius^2

Question 47

Two angles that add up to 180 degrees are called:

Accepted Answer

Supplementary angles

Answer

Complementary angles

Answer

Vertical angles

Answer

Adjacent angles

Question 48

What does it mean for two shapes to be congruent?

Accepted Answer

They have the same size and shape.

Answer

They have the same shape only.

Answer

They have the same size only.

Answer

They have the same position.

Question 49

A circle has a diameter of 12 cm. What is its circumference? Use π = 3.14.

Accepted Answer

37.68 cm

Answer

113.04 cm

Answer

18.84 cm

Answer

75.36 cm

Question 50

Which of the following transformations represents a reflection in the x-axis?

Accepted Answer

(x, y) → (x, -y)

Answer

(x, y) → (y, x)

Answer

(x, y) → (-x, y)

Answer

(x, y) → (-x, -y)

Question 51

Two angles are supplementary. If one angle measures 125°, what is the measure of the other angle?

Accepted Answer

55°

Answer

135°

Answer

235°

Answer

65°

Question 52

A rectangle has a length of 8 cm and a width of 5 cm. What is its area?

Accepted Answer

40 cm²

Answer

30 cm²

Answer

26 cm²

Answer

45 cm²

Question 53

Which of these sets of angles could be the interior angles of a triangle?

Accepted Answer

60°, 70°, 50°

Answer

40°, 50°, 60°

Answer

100°, 120°, 140°

Answer

90°, 90°, 10°

Question 54

What is the name of the line segment that connects two points on a circle and passes through the center?

Accepted Answer

Diameter

Answer

Radius

Answer

Circumference

Answer

Chord

Question 55

A shape undergoes a rotation of 90° clockwise about the origin. Which statement accurately describes the resulting transformation?

Accepted Answer

The shape's orientation changes, while its size and shape remain unchanged.

Answer

The shape's size changes, but its orientation and shape do not.

Answer

The shape's shape changes, but its size and orientation do not.

Question 56

Given two similar triangles, their corresponding sides have a ratio of 2:3. How does the ratio of their areas compare?

Accepted Answer

4:9

Answer

3:2

Answer

2:3

Answer

6:9

Question 57

In a triangle, the angles measure 2x, 3x, and 5x. Determine the value of x.

Accepted Answer

18

Answer

54

Answer

9

Answer

36

Question 58

Which transformation alters the shape of a figure?

Accepted Answer

Non-uniform scaling

Answer

Translation

Answer

Reflection

Answer

Rotation

Question 59

A circle's radius measures 7 cm. Using the approximation π ≈ 22/7, calculate its circumference.

Accepted Answer

44 cm

Answer

14 cm

Answer

22 cm

Answer

154 cm

Question 60

Two angles are supplementary, and one angle is twice the size of the other. Find the measure of the smaller angle.

Accepted Answer

60°

Answer

30°

Answer

45°

Answer

120°

Question 61

A line segment connects the center of a circle to a point on the circle's circumference. What is this line segment called?

Accepted Answer

Radius

Answer

Chord

Answer

Tangent

Answer

Diameter

Question 62

Determine the sum of the interior angles of a hexagon.

Accepted Answer

720°

Answer

360°

Answer

540°

Answer

900°

Question 63

Given a rectangle with a length of 12 cm and a width of 5 cm, what is its area?

Accepted Answer

60 cm²

Answer

24 cm²

Answer

34 cm²

Answer

17 cm²

Question 64

Point A has coordinates (3, -2). After reflection across the y-axis, what are the coordinates of its image, A'?

Accepted Answer

(-3, -2)

Answer

(-2, 3)

Answer

(3, 2)

Answer

(-3, 2)