Properties of geometrical figures

Identify and apply properties of triangles and quadrilaterals.

Space · MA4-GEO-C-01

Sub-topics

Triangles

Classify triangles by their sides and angles, and find missing angles using the angle sum property.

Quadrilaterals

Identify and classify quadrilaterals by their properties, and find missing angles using the angle sum of a quadrilateral.

Open Math

Properties of geometrical figures

Space · MA4-GEO-C-01

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Date:

Triangles

Q1Straightforward

A triangle has all three sides equal in length. What type of triangle is it?

A.Scalene
B.Isosceles
C.Equilateral
D.Right-angled

Q2Straightforward

A triangle has exactly two equal sides. What type of triangle is it?

A.Scalene
B.Isosceles
C.Equilateral
D.Obtuse

Q3Straightforward

A triangle contains one angle of exactly

90°

. How is this triangle classified by its angles?

A.Acute
B.Obtuse
C.Right-angled
D.Equilateral

Q4Straightforward

A triangle has angles of

50°

70°

, and

60°

. How is this triangle classified by its angles?

A.Acute
B.Right-angled
C.Obtuse
D.Isosceles

Q5Moderate

Two angles of a triangle are

55°

and

70°

. Find the third angle in degrees.

Q6Moderate

Two angles of a triangle are

90°

and

35°

. Find the third angle in degrees.

Q7Moderate

Two angles of a triangle are

48°

and

63°

. Find the third angle in degrees.

Q8Moderate

An isosceles triangle has two equal base angles of

65°

each. Find the apex angle in degrees.

Q9Challenging

The angles of a triangle are in the ratio

1:2:3

. Find the largest angle in degrees.

Q10Challenging

An isosceles triangle has an apex angle of

40°

. Find the size of each base angle in degrees.

Q11Challenging

In a triangle, one angle is twice another angle. The third angle is

60°

. Find the smallest angle in degrees.

Q12Challenging

A right-angled isosceles triangle has one angle of

90°

and the other two angles are equal. Find the size of each equal angle in degrees.

Quadrilaterals

Q13Straightforward

A quadrilateral has four right angles and all four sides equal. What type of quadrilateral is it?

A.Rectangle
B.Rhombus
C.Square
D.Parallelogram

Q14Straightforward

A quadrilateral has four right angles. Its opposite sides are equal in length, but not all four sides are equal. What type of quadrilateral is it?

A.Square
B.Rhombus
C.Trapezium
D.Rectangle

Q15Straightforward

A quadrilateral has exactly one pair of parallel sides. What type of quadrilateral is it?

A.Parallelogram
B.Trapezium
C.Rhombus
D.Kite

Q16Straightforward

A quadrilateral has all four sides equal in length but no right angles. What type of quadrilateral is it?

A.Square
B.Rectangle
C.Trapezium
D.Rhombus

Q17Moderate

Three angles of a quadrilateral are

80°

100°

, and

120°

. Find the fourth angle in degrees.

Q18Moderate

One angle of a rectangle is labelled

(2x + 10)°

. Find the value of

x

Q19Moderate

A parallelogram has one angle of

65°

. Find the size of the opposite angle in degrees.

Q20Moderate

Three angles of a trapezium are

72°

108°

, and

95°

. Find the fourth angle in degrees.

Q21Challenging

A rhombus has one angle of

3x°

and an adjacent angle of

(x + 20)°

. Find the value of

x

Q22Challenging

In a parallelogram, one angle is twice the size of the adjacent angle. Find the size of the larger angle in degrees.

Q23Challenging

The four angles of a quadrilateral are in the ratio

2:3:4:6

. Find the size of the largest angle in degrees.

Q24Challenging

Three of the four angles in a quadrilateral are

90°

2x°

, and

3x°

, and the fourth angle is

x°

. Find the value of

x

Worked solutions and answers at openmath.au/year-7/geometrical-figures