Geometry Quizzes: Master Shapes and Angles in Year 11 Maths

Question 1

Prove that the sum of the interior angles of a quadrilateral is 360 degrees. Explain your reasoning.

Accepted Answer

Divide the quadrilateral into two triangles and use the fact that the sum of the interior angles of a triangle is 180 degrees.

Answer

Measure the four angles of the quadrilateral and add them up.

Answer

Use the Pythagorean theorem to relate the lengths of the sides of the quadrilateral to the interior angles.

Question 2

To prove that the sum of the interior angles of a quadrilateral is 360 degrees, which method should you use?

Accepted Answer

Divide the quadrilateral into two triangles and apply the angle sum property of triangles.

Answer

The sum of exterior angles of a quadrilateral is 360 degrees, so the sum of interior angles must also be 360 degrees.

Answer

The sum of the interior angles of a quadrilateral depends on its specific shape and cannot be determined without knowing more about it.

Question 3

Theorem for Triangle Angle Sum: Which theorem states that the sum of the interior angles of a triangle equals 180 degrees?

Accepted Answer

Triangle Angle Sum Theorem

Answer

Pythagorean Theorem

Answer

Congruence Theorem

Answer

Parallel Lines Theorem

Question 4

Which transformation does NOT preserve shape?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 5

Solid with Triangular Base and Lateral Faces: Which solid has a triangular base and triangular lateral faces?

Accepted Answer

Pyramid

Answer

Cone

Answer

Cylinder

Answer

Sphere

Question 6

What is the gradient of a line that is horizontal?

Accepted Answer

0

Answer

1

Answer

Undefined

Answer

Varies

Question 7

Determine the surface area of a sphere with a radius of 4 cm.

Accepted Answer

32π cm²

Answer

16π cm²

Answer

64π cm²

Answer

128π cm²

Question 8

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

Accepted Answer

540 degrees

Answer

360 degrees

Answer

720 degrees

Answer

1080 degrees

Question 9

Find the equation of a straight line passing through points (2, 3) and (5, 7).

Accepted Answer

y = 2x + 1

Answer

y = x + 1

Answer

y = 2x - 1

Answer

y = x - 1

Question 10

Which characteristic is NOT a property of a parallelogram?

Accepted Answer

All sides are congruent.

Answer

Opposite sides are parallel.

Answer

Opposite angles are equal.

Answer

Diagonals bisect each other.

Question 11

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

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 12

What is the definition of a regular polygon?

Accepted Answer

A two-dimensional figure with all sides equal in length and all angles equal in measure.

Answer

A polygon with only equal sides.

Answer

A polygon with only equal angles.

Answer

A polygon with all sides parallel and all angles right angles.

Question 13

What is the Pythagoras' theorem used for?

Accepted Answer

Finding the length of the hypotenuse of a right-angled triangle

Answer

Finding the area of a triangle

Answer

Finding the height of a parallelogram

Answer

Finding the circumference of a circle

Question 14

What is the locus of points that are equidistant from two given points?

Accepted Answer

A circle

Answer

A line

Answer

A parabola

Answer

An ellipse

Question 15

Which of the following is NOT a characteristic 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 16

Which of the following is NOT a Pythagorean triple?

Accepted Answer

(7, 24, 25)

Answer

(3, 4, 5)

Answer

(5, 12, 13)

Answer

(6, 8, 10)

Question 17

Which of the following is the equation of a circle with center (2, -1) and radius 3?

Accepted Answer

(x + 2)² + (y - 1)² = 9

Answer

x² + y² = 3

Answer

(x - 2)² + (y + 1)² = 3

Answer

x² + y² - 4x + 2y = -3

Question 18

Find the volume of a rectangular prism with the following dimensions: length = 5 cm, width = 3 cm, height = 4 cm.

Accepted Answer

60 cm³

Answer

20 cm³

Answer

30 cm³

Answer

80 cm³

Question 19

Find the slope of the line perpendicular to the line y = 2x + 3.

Accepted Answer

-1/2

Answer

1/2

Answer

-2

Answer

2

Question 20

Which type of triangle has all sides congruent?

Accepted Answer

Equilateral triangle

Answer

Right triangle

Answer

Scalene triangle

Answer

Isosceles triangle

Question 21

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

Accepted Answer

It has 5 sides

Answer

Its opposite angles are equal

Answer

It has 4 equal sides

Question 22

What is the measure of each interior angle of a regular pentagon?

Accepted Answer

108°

Answer

72°

Answer

120°

Answer

144°

Question 23

A circle has a radius of 10 cm. What is its circumference?

Accepted Answer

20π cm

Answer

10π cm

Answer

40π cm

Answer

50π cm

Question 24

Which of the following transformations preserves the size and shape of a figure?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 25

What is the area of a triangle with a base of 12 cm and a height of 8 cm?

Accepted Answer

48 cm²

Answer

144 cm²

Answer

24 cm²

Answer

96 cm²

Question 26

Which of the following is the equation of a line passing through the points (2, 3) and (4, 7)?

Accepted Answer

y = 2x + 1

Answer

y = 2x - 1

Answer

y = x + 5

Answer

y = x - 3

Question 27

What is the volume of a cube with an edge length of 5 cm?

Accepted Answer

125 cm³

Answer

625 cm³

Answer

25 cm³

Question 28

Which of the following is a Pythagorean triple?

Accepted Answer

(3, 4, 5)

Answer

(2, 3, 6)

Answer

(5, 12, 13)

Answer

(6, 8, 10)

Question 29

What is the surface area of a sphere with a radius of 6 cm?

Accepted Answer

36π cm²

Answer

72π cm²

Answer

12π cm²

Answer

144π cm²

Question 30

Which of the following is a regular polyhedron with 12 faces and 30 edges?

Accepted Answer

Dodecahedron

Answer

Icosahedron

Answer

Octahedron

Answer

Cube

Question 31

A triangle with angles measuring 60°, 60°, and 60° is classified as:

Accepted Answer

Equilateral

Answer

Scalene

Answer

Isosceles

Answer

Right-angled

Question 32

The sum of the interior angles of a pentagon is:

Accepted Answer

540°

Answer

720°

Answer

360°

Answer

900°

Question 33

A rectangle with all sides equal is called a:

Accepted Answer

Square

Answer

Parallelogram

Answer

Trapezium

Answer

Rhombus

Question 34

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

Accepted Answer

10π cm

Answer

20π cm

Answer

5π cm

Answer

25π cm

Question 35

Two lines that intersect at a right angle are called:

Accepted Answer

Perpendicular lines

Answer

Transversal lines

Answer

Parallel lines

Answer

Intersecting lines

Question 36

A shape that can be divided into two congruent halves by a line of symmetry is called:

Accepted Answer

Symmetrical

Answer

Regular

Answer

Asymmetrical

Answer

Irregular

Question 37

A 180° rotation of a shape about a point results in:

Accepted Answer

A reflection

Answer

A congruent shape

Answer

A translation

Answer

A dilation

Question 38

The area of a parallelogram with a base of 8 cm and a height of 5 cm is:

Accepted Answer

40 cm²

Answer

20 cm²

Answer

13 cm²

Answer

64 cm²

Question 39

A cube with a side length of 6 cm has a volume of:

Accepted Answer

216 cm³

Answer

72 cm³

Answer

36 cm³

Answer

144 cm³

Question 40

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

Accepted Answer

Hypotenuse

Answer

Base

Answer

Perpendicular

Answer

Altitude