Sec 2 G1 Maths Triangles and quadrilaterals worksheet with answers

A free Sec 2 G1 Maths worksheet on triangles and quadrilaterals: 10 questions, 31 marks, short questions first and then structured ones, in the school exam style. The answers and full worked solutions are on the last page.

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Sec 2 G1 Maths worksheet: Triangles and quadrilaterals

Total: 31 marksSuggested time: 55 minutes

Name: ______________________________Class: ____________ Date: ____________

Answer all questions. Show all your working. Give non-exact answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless the question says otherwise.

Section A

In the diagram, the bisector of

\angle ABC

has been constructed with compasses, and

Q

is a point on it.

QM

is perpendicular to

BA

and

QN

is perpendicular to

BC

. Find

x

Answercm[1]

The marks on the diagram show what is known about quadrilateral

ABCD

. Write down the most special name of

ABCD

Answer[1]

The marks on the diagram show what is known about quadrilateral

ABCD

. Write down the most special name of

ABCD

Answer[1]

ABCD

is a trapezium with

AB

parallel to

DC

. Find

x

Answer[2]

ABC

is an equilateral triangle and

D

lies on

BC

. Find

x

Answer[2]

Construct quadrilateral

ABCD

with

AB = 5

cm,

BC = 7

cm,

CD = 5

cm,

DA = 6

cm and the diagonal

AC = 7

cm. Measure the length of the diagonal

BD

, to the nearest

0.1

cm.

Answercm[2]

ABCD

is a kite with

AB = AD

and

CB = CD

. Find

x

Answer[2]

(a)Construct quadrilateral

ABCD

with

AB = 4

cm,

BC = 6

cm,

CD = 7

cm,

DA = 5

cm and the diagonal

AC = 9

cm. Measure the length of the diagonal

BD

, to the nearest

0.1

cm.

Answer (a)cm[2]

(b)Construct quadrilateral

ABCD

with

AB = 6

cm,

\angle DAB = 105^\circ

AD = 4

cm,

\angle ABC = 90^\circ

and

BC = 5

cm. Measure the length of

CD

, to the nearest

0.1

cm.

Answer (b)cm[2]

Section B

(a)The diagram shows a quadrilateral

ABCD

. Find

x

Answer (a)[2]

(b)

A

is the point

(0, 5)

and

B

is the point

(6, 5)

. The point

P

lies on the perpendicular bisector of

AB

and on the line

y = 1

. Find the

x

-coordinate of

P

Answer (b)[2]

(c)Construct quadrilateral

ABCD

with

AB = 6

cm,

BC = 5

cm,

CD = 5

cm,

DA = 6

cm and the diagonal

AC = 7

cm. Measure the length of the diagonal

BD

, to the nearest

0.1

cm.

Answer (c)cm[2]

(d)In triangle

LMN

LM = LN

. Find

x

Answer (d)[2]

(a)

ABCD

is a rectangle. Its diagonals meet at

O

, and

\angle OAB = 52^\circ

. Find

x

Answer (a)°[2]

(b)

ABCD

is a kite with

AB = AD

and

CB = CD

. Find

x

Answer (b)[2]

(c)(i)Construct triangle

ABC

with

AB = 9

cm,

BC = 7

cm and

CA = 6

cm. Measure

\angle ACB

, to the nearest degree.

Answer (c)(i)°[2]

(c)(ii)Construct triangle

ABC

with

AB = 6

cm,

\angle BAC = 70^\circ

and

\angle ABC = 60^\circ

. Measure the length of

AC

, to the nearest

0.1

cm.

Answer (c)(ii)cm[2]

END OF PAPER

Answers and worked solutions

Question 1

Answer:

x = 4

cm[1]

QN = QM

(

Q

is on the bisector of

\angle ABC

)

x = 4

Question 2

Answer: rectangle[1]

Equal sides: two pairs opposite.Parallel sides: none marked.Right angles: yes.Four right angles (opposite sides equal), but the sides are not all equal: a rectangle.

Question 3

Answer: square[1]

Equal sides: all four.Parallel sides: none marked.Right angles: yes.Four equal sides and right angles: a square.

Question 4

Answer:

x = 103

[2]

x^\circ + 77^\circ = 180^\circ

(int. ∠s,

AB \parallel DC

)

x = 180 - 77

x = 103

Question 5

Answer:

x = 102

(∠ sum of △)[2]

\angle ABC = 60^\circ

(equil. △)

60^\circ + 18^\circ + x^\circ = 180^\circ

x = 180 - 60 - 18

x = 102

(∠ sum of △)

Question 6

Answer:

BD = 9.2

cm (to the nearest

0.1

cm)[2]

Draw

AC = 7

cm.Arcs of radius

5

cm about

A

and

7

cm about

C

cross at

B

.Arcs of radius

6

cm about

A

and

5

cm about

C

cross at

D

, on the other side of

AC

from

B

BD = 9.2

cm (to the nearest

0.1

cm)

Question 7

Answer:

x = 99

(∠ sum of quad.)[2]

\angle ADC = \angle ABC

\phantom{\angle ADC} = x^\circ

(

AC

is a line of symmetry of the kite)

88^\circ + x^\circ + 74^\circ + x^\circ = 360^\circ

2x = 198

x = 99

(∠ sum of quad.)

Question 8

(a)Answer:

BD = 6.0

cm (to the nearest

0.1

cm)[2]

Draw

AC = 9

cm.Arcs of radius

4

cm about

A

and

6

cm about

C

cross at

B

.Arcs of radius

5

cm about

A

and

7

cm about

C

cross at

D

, on the other side of

AC

from

B

BD = 6.0

cm (to the nearest

0.1

cm)

(b)Answer:

CD = 7.1

cm (to the nearest

0.1

cm)[2]

Draw

AB = 6

cm.At

A

, measure

\angle DAB = 105^\circ

, draw a ray and mark

D

on it with

AD = 4

cm.At

B

, measure

\angle ABC = 90^\circ

, draw a ray and mark

C

on it with

BC = 5

cm.

CD = 7.1

cm (to the nearest

0.1

cm)

Question 9

(a)Answer:

x = 91

(∠ sum of quad.)[2]

75^\circ + 88^\circ + x^\circ + 106^\circ = 360^\circ

x = 360 - 75 - 88 - 106

x = 91

(∠ sum of quad.)

(b)Answer: The

x

-coordinate of

P

3

.[2]

\mathstrut x = \dfrac{0 + 6}{2}

x = 3

The

x

-coordinate of

P

3

(c)Answer:

BD = 8.4

cm (to the nearest

0.1

cm)[2]

Draw

AC = 7

cm.Arcs of radius

6

cm about

A

and

5

cm about

C

cross at

B

.Arcs of radius

6

cm about

A

and

5

cm about

C

cross at

D

, on the other side of

AC

from

B

BD = 8.4

cm (to the nearest

0.1

cm)

(d)Answer:

x = 37

(∠ sum of △)[2]

\angle LNM = x^\circ

(base ∠s of isos. △)

x^\circ + x^\circ + 106^\circ = 180^\circ

2x = 74

x = 37

(∠ sum of △)

Question 10

(a)Answer:

x = 38

°[2]

\angle OBA = 52^\circ

(base ∠s of isos. △)

x = 90 - 52

x = 38

(b)Answer:

x = 111

(∠ sum of quad.)[2]

\angle ADC = \angle ABC

\phantom{\angle ADC} = x^\circ

(

AC

is a line of symmetry of the kite)

64^\circ + x^\circ + 74^\circ + x^\circ = 360^\circ

2x = 222

x = 111

(∠ sum of quad.)

(c)(i)Answer:

\angle ACB = 87^\circ

(to the nearest degree) °[2]

Draw

AB = 9

cm.With centre

A

and radius

AC = 6

cm, draw an arc.With centre

B

and radius

BC = 7

cm, draw an arc to cut the first one at

C

. Join

AC

and

BC

\angle ACB = 87^\circ

(to the nearest degree)

(c)(ii)Answer:

AC = 6.8

cm (to the nearest

0.1

cm)[2]

Draw

AB = 6

cm.At

A

, measure

\angle BAC = 70^\circ

and draw a ray.At

B

, measure

\angle ABC = 60^\circ

and draw a ray. The rays cross at

C

AC = 6.8

cm (to the nearest

0.1

cm)

Sec 2 G1 Maths Triangles and quadrilaterals worksheet with answers

In the print window, choose Save as PDF to download it.

Or practise it online with step-by-step help when you get one wrong.

Section B

(a)The diagram shows a quadrilateral

ABCD

. Find

x

Answer (a)[2]

(b)

A

is the point

(0, 5)

and

B

is the point

(6, 5)

. The point

P

lies on the perpendicular bisector of

AB

and on the line

y = 1

. Find the

x

-coordinate of

P

Answer (b)[2]

(c)Construct quadrilateral

ABCD

with

AB = 6

cm,

BC = 5

cm,

CD = 5

cm,

DA = 6

cm and the diagonal

AC = 7

cm. Measure the length of the diagonal

BD

, to the nearest

0.1

cm.

Answer (c)cm[2]

(d)In triangle

LMN

LM = LN

. Find

x

Answer (d)[2]

Answers and worked solutions

Question 1

Answer:

x = 4

cm[1]

QN = QM

(

Q

is on the bisector of

\angle ABC

)

x = 4

Question 2

Answer: rectangle[1]

Equal sides: two pairs opposite.Parallel sides: none marked.Right angles: yes.Four right angles (opposite sides equal), but the sides are not all equal: a rectangle.

Question 3

Answer: square[1]

Equal sides: all four.Parallel sides: none marked.Right angles: yes.Four equal sides and right angles: a square.

Question 4

Answer:

x = 103

[2]

x^\circ + 77^\circ = 180^\circ

(int. ∠s,

AB \parallel DC

)

x = 180 - 77

x = 103

Question 5

Answer:

x = 102

(∠ sum of △)[2]

\angle ABC = 60^\circ

(equil. △)

60^\circ + 18^\circ + x^\circ = 180^\circ

x = 180 - 60 - 18

x = 102

(∠ sum of △)

Question 6

Answer:

BD = 9.2

cm (to the nearest

0.1

cm)[2]

Draw

AC = 7

cm.Arcs of radius

5

cm about

A

and

7

cm about

C

cross at

B

.Arcs of radius

6

cm about

A

and

5

cm about

C

cross at

D

, on the other side of

AC

from

B

BD = 9.2

cm (to the nearest

0.1

cm)

Question 7

Answer:

x = 99

(∠ sum of quad.)[2]

\angle ADC = \angle ABC

\phantom{\angle ADC} = x^\circ

(

AC

is a line of symmetry of the kite)

88^\circ + x^\circ + 74^\circ + x^\circ = 360^\circ

2x = 198

x = 99

(∠ sum of quad.)

Question 8

(a)Answer:

BD = 6.0

cm (to the nearest

0.1

cm)[2]

Draw

AC = 9

cm.Arcs of radius

4

cm about

A

and

6

cm about

C

cross at

B

.Arcs of radius

5

cm about

A

and

7

cm about

C

cross at

D

, on the other side of

AC

from

B

BD = 6.0

cm (to the nearest

0.1

cm)

(b)Answer:

CD = 7.1

cm (to the nearest

0.1

cm)[2]

Draw

AB = 6

cm.At

A

, measure

\angle DAB = 105^\circ

, draw a ray and mark

D

on it with

AD = 4

cm.At

B

, measure

\angle ABC = 90^\circ

, draw a ray and mark

C

on it with

BC = 5

cm.

CD = 7.1

cm (to the nearest

0.1

cm)

Question 9

(a)Answer:

x = 91

(∠ sum of quad.)[2]

75^\circ + 88^\circ + x^\circ + 106^\circ = 360^\circ

x = 360 - 75 - 88 - 106

x = 91

(∠ sum of quad.)

(b)Answer: The

x

-coordinate of

P

3

.[2]

\mathstrut x = \dfrac{0 + 6}{2}

x = 3

The

x

-coordinate of

P

3

(c)Answer:

BD = 8.4

cm (to the nearest

0.1

cm)[2]

Draw

AC = 7

cm.Arcs of radius

6

cm about

A

and

5

cm about

C

cross at

B

.Arcs of radius

6

cm about

A

and

5

cm about

C

cross at

D

, on the other side of

AC

from

B

BD = 8.4

cm (to the nearest

0.1

cm)

(d)Answer:

x = 37

(∠ sum of △)[2]

\angle LNM = x^\circ

(base ∠s of isos. △)

x^\circ + x^\circ + 106^\circ = 180^\circ

2x = 74

x = 37

(∠ sum of △)

Question 10

(a)Answer:

x = 38

°[2]

\angle OBA = 52^\circ

(base ∠s of isos. △)

x = 90 - 52

x = 38

(b)Answer:

x = 111

(∠ sum of quad.)[2]

\angle ADC = \angle ABC

\phantom{\angle ADC} = x^\circ

(

AC

is a line of symmetry of the kite)

64^\circ + x^\circ + 74^\circ + x^\circ = 360^\circ

2x = 222

x = 111

(∠ sum of quad.)

(c)(i)Answer:

\angle ACB = 87^\circ

(to the nearest degree) °[2]

Draw

AB = 9

cm.With centre

A

and radius

AC = 6

cm, draw an arc.With centre

B

and radius

BC = 7

cm, draw an arc to cut the first one at

C

. Join

AC

and

BC

\angle ACB = 87^\circ

(to the nearest degree)

(c)(ii)Answer:

AC = 6.8

cm (to the nearest

0.1

cm)[2]

Draw

AB = 6

cm.At

A

, measure

\angle BAC = 70^\circ

and draw a ray.At

B

, measure

\angle ABC = 60^\circ

and draw a ray. The rays cross at

C

AC = 6.8

cm (to the nearest

0.1

cm)