Angles and Shapes: Master Geometry Concepts for Year 11 Maths

Question 1

Which of the following is a quadrilateral with exactly one pair of parallel sides?

Accepted Answer

Trapezoid

Answer

Parallelogram

Answer

Rectangle

Answer

Rhombus

Question 2

Which of the following transformations involves a change in both shape and size?

Accepted Answer

Dilation

Answer

Rotation

Answer

Translation

Answer

Reflection

Question 3

Two triangles are congruent if they have:

Accepted Answer

Two pairs of equal sides and one pair of equal angles

Answer

Three pairs of equal sides

Answer

Three pairs of equal angles

Answer

One pair of equal sides and two pairs of equal angles

Question 4

Which of the following is a regular polygon with 8 sides?

Accepted Answer

Octagon

Answer

Square

Answer

Pentagon

Answer

Hexagon

Question 5

Determine the length of the hypotenuse of a right-angled triangle with legs measuring 3 cm and 4 cm.

Accepted Answer

7 cm

Answer

5 cm

Answer

12 cm

Answer

16 cm

Question 6

Which of the following is considered a regular polygon?

Accepted Answer

A polygon with equal sides and angles

Answer

A quadrilateral with equal sides

Answer

A polygon with perpendicular sides

Answer

A polygon with angles greater than 90 degrees

Question 7

Which of the following shapes is three-dimensional?

Accepted Answer

Cube

Answer

Circle

Answer

Triangle

Answer

Square

Question 8

Determine the surface area of a sphere with a radius of 5 cm.

Accepted Answer

100π cm²

Answer

25π cm²

Answer

50π cm²

Answer

200π cm²

Question 9

What is the interior angle sum of a regular pentagon?

Accepted Answer

540°

Answer

360°

Answer

720°

Answer

900°

Question 10

Which condition ensures that two triangles are congruent?

Accepted Answer

Identical shape and size

Answer

Equal perimeters

Answer

Equal areas

Answer

Equal number of sides

Question 11

Determine the measurement of an exterior angle in a regular hexagon

Accepted Answer

120°

Answer

60°

Answer

180°

Answer

240°

Question 12

Which transformation is NOT considered a similarity transformation?

Accepted Answer

Translation

Answer

Enlargement

Answer

Reduction

Answer

Rotation

Question 13

Select the statement that correctly describes the sum of complementary angles:

Accepted Answer

They add up to 90 degrees.

Answer

They add up to 180 degrees.

Answer

They add up to 270 degrees.

Answer

They add up to 360 degrees.

Question 14

How many sides does a regular hexagon have?

Accepted Answer

6

Answer

4

Answer

8

Answer

10

Question 15

Which of the following is a characteristic of a parallelogram?

Accepted Answer

It possesses all of the above characteristics

Answer

Opposite sides are parallel.

Answer

Opposite sides are equal in length.

Answer

Diagonals bisect each other.

Question 16

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

Accepted Answer

25π cm²

Answer

50π cm²

Answer

75π cm²

Answer

100π cm²

Question 17

Which theorem CANNOT be used to prove that two triangles are congruent?

Accepted Answer

Angle-Angle-Angle (AAA) Theorem

Answer

Side-Side-Side (SSS) Theorem

Answer

Angle-Side-Angle (ASA) Theorem

Answer

Hypotenuse-Leg (HL) Theorem

Question 18

Which statement about parallelograms is false?

Accepted Answer

Diagonals do not bisect each other.

Answer

Opposite sides are parallel and equal in length.

Answer

Opposite angles are equal in measure.

Answer

Adjacent angles are supplementary.

Question 19

Find the sum of the interior angles of a hexagon.

Accepted Answer

720°

Answer

360°

Answer

540°

Answer

900°

Question 20

Which of the following is a chord of a circle?

Accepted Answer

A line segment connecting two points on the circle

Answer

A line segment intersecting the circle at one point

Answer

A line passing through the center of the circle

Answer

A line tangent to the circle

Question 21

Which of the following is NOT a type of triangle?

Accepted Answer

Obtuse

Answer

Equilateral

Answer

Isosceles

Answer

Scalene

Question 22

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

Accepted Answer

360 degrees

Answer

180 degrees

Answer

270 degrees

Answer

540 degrees

Question 23

Which of the following is NOT a regular polygon?

Accepted Answer

Circle

Answer

Square

Answer

Rectangle

Answer

Equilateral triangle

Question 24

What is the Pythagorean theorem?

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

c² - a² = b²

Answer

c² - b² = a²

Question 25

If two triangles are congruent by SAS, which of the following statements is valid?

Accepted Answer

The triangles have two pairs of equal angles and one pair of equal sides.

Answer

The triangles have three pairs of equal sides.

Answer

The triangles have three pairs of equal angles.

Answer

The triangles are not necessarily congruent.

Question 26

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

Accepted Answer

Adjacent sides are perpendicular

Answer

Opposite sides are parallel and equal in length

Answer

Opposite angles are equal

Answer

Diagonals bisect each other

Question 27

In a right-angled triangle, which theorem relates the lengths of its sides?

Accepted Answer

Pythagorean theorem

Answer

Cosine rule

Answer

Sine rule

Answer

Area of a triangle theorem

Question 28

What is the area of a circle with a radius of 5 cm?

Accepted Answer

25π cm²

Answer

50π cm²

Answer

75π cm²

Answer

100π cm²

Question 29

Find the volume of a cone with a radius of 4 cm and a height of 10 cm.

Accepted Answer

64π cm³

Answer

32π cm³

Answer

128π cm³

Answer

256π cm³

Question 30

What is the probability of rolling a 6 on a standard six-sided die?

Accepted Answer

1/6

Answer

1/2

Answer

1/3

Answer

1/4

Question 31

Which property is NOT characteristic of a parallelogram?

Accepted Answer

Adjacent angles are complementary.

Answer

Opposite sides are parallel and of equal length.

Answer

Opposite angles are of equal measure.

Answer

Diagonals bisect each other.

Question 32

For two triangles to be congruent by SAS, they must have

Accepted Answer

Two sides and the included angle congruent.

Answer

Two angles and the included side congruent.

Answer

Three sides congruent.

Answer

Three angles congruent.

Question 33

The area of a circle with a radius of 5 cm is

Accepted Answer

25π cm²

Answer

50π cm²

Answer

100π cm²

Answer

200π cm²

Question 34

Which polygon has all sides and angles equal?

Accepted Answer

Rhombus

Answer

Rectangle

Answer

Trapezoid

Answer

Isosceles triangle

Question 35

The Pythagorean theorem is primarily used for

Accepted Answer

Finding the length of a side of a right triangle

Answer

Finding the area of a circle

Answer

Finding the volume of a sphere

Answer

Finding the surface area of a cone

Question 36

In a triangle, the sum of the interior angles equals

Accepted Answer

180 degrees

Answer

90 degrees

Answer

270 degrees

Answer

360 degrees

Question 37

In a congruent triangle, corresponding parts are

Accepted Answer

Equal in length and angle measure

Answer

Equal in length but not in angle measure

Answer

Equal in angle measure but not in length

Answer

Not necessarily equal

Question 38

The midpoint of a line segment divides the segment into two

Accepted Answer

Congruent halves

Answer

Equal but not congruent halves

Answer

Incommensurate parts

Answer

Unequal parts

Question 39

Which of the following is NOT a factor that can affect the area of a triangle?

Accepted Answer

Perimeter

Answer

Base length

Answer

Height

Answer

Angle between the base and height

Question 40

In a regular polygon, all angles are:

Accepted Answer

Congruent

Answer

Similar

Answer

Equal in measure but not similar

Answer

Parallel

Question 41

Which of the following is a characteristic of an isosceles triangle?

Accepted Answer

Two equal sides

Answer

Three equal sides

Answer

Four equal sides

Answer

No equal sides

Question 42

The Pythagorean theorem is used to calculate the length of the

Accepted Answer

Longest side of a right-angled triangle

Answer

Shortest side of a right-angled triangle

Answer

Height of a right-angled triangle

Answer

Area of a right-angled triangle

Question 43

The angle at the center of a circle that intercepts an arc of 120 degrees measures

Accepted Answer

120 degrees

Answer

60 degrees

Answer

90 degrees

Answer

180 degrees

Question 44

Which of the following is a property of a circle?

Accepted Answer

The distance from the center to any point on the circle is constant.

Answer

Opposite angles are equal.

Answer

The sum of the interior angles is 360 degrees.

Answer

The diagonals bisect each other.

Question 45

What is the area of a triangle with a base of 8 cm and a height of 6 cm?

Accepted Answer

24 cm^2

Answer

12 cm^2

Answer

36 cm^2

Answer

48 cm^2

Question 46

What is the radius of a circle with a diameter of 10 cm?

Accepted Answer

5 cm

Answer

2.5 cm

Answer

10 cm

Answer

20 cm

Question 47

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

Accepted Answer

Angle-Angle-Side

Answer

Side-Side-Side

Answer

Angle-Side-Angle

Answer

Side-Angle-Side

Question 48

A triangle has angles measuring x, 2x, and 3x degrees. What is the value of x?

Accepted Answer

18

Answer

20

Answer

30

Answer

15

Question 49

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

Accepted Answer

60 degrees

Answer

120 degrees

Answer

30 degrees

Answer

45 degrees

Question 50

A regular polygon has interior angles that each measure 140 degrees. How many sides does the polygon have?

Accepted Answer

9

Answer

8

Answer

7

Answer

12

Question 51

A quadrilateral has angles measuring 80 degrees, 100 degrees, and 110 degrees. What is the measure of the fourth angle?

Accepted Answer

70 degrees

Answer

80 degrees

Answer

100 degrees

Answer

90 degrees

Question 52

Two triangles are similar. The sides of the smaller triangle are 4cm, 5cm, and 6cm. The longest side of the larger triangle is 15cm. What is the perimeter of the larger triangle?

Accepted Answer

45cm

Answer

20cm

Answer

50cm

Answer

30cm

Question 53

Which of the following statements is true about a rhombus?

Accepted Answer

Its diagonals bisect each other at right angles.

Answer

It has at least one right angle.

Answer

All its angles are equal.

Answer

Opposite angles are supplementary.

Question 54

A circle has a radius of 5cm. What is its circumference?

Accepted Answer

31.4cm

Answer

15.7cm

Answer

157cm

Answer

78.5cm

Question 55

A sector of a circle with a radius of 8cm has a central angle of 60 degrees. What is the area of the sector?

Accepted Answer

16π cm²

Answer

32π cm²

Answer

8π cm²

Answer

4π cm²

Question 56

Which of the following sets of angles could be the exterior angles of a triangle?

Accepted Answer

40 degrees, 60 degrees, 80 degrees

Answer

30 degrees, 60 degrees, 90 degrees

Answer

20 degrees, 70 degrees, 110 degrees

Answer

40 degrees, 50 degrees, 100 degrees

Question 57

Two congruent triangles are placed together to form a parallelogram. If each triangle has a base of 10cm and a height of 8cm, what is the area of the parallelogram?

Accepted Answer

80cm²

Answer

40cm²

Answer

320cm²

Answer

160cm²