Sec 2 G1 Maths Congruence and similarity worksheet with answers

A free Sec 2 G1 Maths worksheet on congruence and similarity: 8 questions, 30 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: Congruence and similarity

Total: 30 marksSuggested time: 50 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,

D

lies on

AB

and

E

lies on

AC

, with

DE

parallel to

BC

. Find

DE

Answercm[3]

In the diagram,

D

lies on

AB

and

E

lies on

AC

, with

DE

parallel to

BC

. Find

DE

, correct to 3 significant figures.

Answercm[3]

In the diagram,

D

lies on

AB

and

E

lies on

AC

, with

DE

parallel to

BC

. Find

DE

, correct to 3 significant figures.

Answercm[3]

In the diagram,

D

lies on

AB

and

E

lies on

AC

, with

DE

parallel to

BC

. Find

DE

, correct to 3 significant figures.

Answercm[3]

In the diagram,

D

lies on

AB

and

E

lies on

AC

, with

DE

parallel to

BC

. Find

DE

, correct to 3 significant figures.

Answercm[3]

Section B

(a)In the diagram, triangle

ABC

is similar to triangle

RQP

. Find

x

Answer (a)cm[2]

(b)In the diagram,

D

lies on

AB

and

E

lies on

AC

, with

DE

parallel to

BC

. Find

DB

, correct to 3 significant figures.

Answer (b)cm[3]

(a)In the diagram, triangle

ABC

is similar to triangle

QPR

. Find

x

Answer (a)cm[2]

(b)In the diagram,

D

lies on

AB

and

E

lies on

AC

, with

DE

parallel to

BC

. Find

DE

Answer (b)cm[3]

(a)In the diagram, triangle

ABC

is similar to triangle

QRP

. Find

x

Answer (a)cm[2]

(b)In the diagram,

D

lies on

AB

and

E

lies on

AC

, with

DE

parallel to

BC

. Find

DE

, correct to 3 significant figures.

Answer (b)cm[3]

END OF PAPER

Answers and worked solutions

Question 1

Answer:

DE = 6.25

cm[3]

\angle ADE = \angle ABC

(corresponding angles)

\angle A

is common, so the triangles are similar (AA).

\mathstrut AB = 5 + 3

AB = 8

\dfrac{DE}{BC} = \dfrac{AD}{AB}

\mathstrut \dfrac{DE}{10} = \dfrac{5}{8}

DE = \dfrac{5}{8} \times 10

DE = 6.25

Question 2

Answer:

\phantom{DE} = 6.67

cm (3 s.f.)[3]

\angle ADE = \angle ABC

(corresponding angles)

\angle A

is common, so the triangles are similar (AA).

\mathstrut AB = 5 + 4

AB = 9

\dfrac{DE}{BC} = \dfrac{AD}{AB}

\mathstrut \dfrac{DE}{12} = \dfrac{5}{9}

DE = \dfrac{5}{9} \times 12

DE = 6.6666\ldots

\phantom{DE} = 6.67

cm (3 s.f.)

Question 3

Answer:

\phantom{DE} = 5.45

cm (3 s.f.)[3]

\angle ADE = \angle ABC

(corresponding angles)

\angle A

is common, so the triangles are similar (AA).

\mathstrut AB = 5 + 6

AB = 11

\dfrac{DE}{BC} = \dfrac{AD}{AB}

\mathstrut \dfrac{DE}{12} = \dfrac{5}{11}

DE = \dfrac{5}{11} \times 12

DE = 5.4545\ldots

\phantom{DE} = 5.45

cm (3 s.f.)

Question 4

Answer:

\phantom{DE} = 5.33

cm (3 s.f.)[3]

\angle ADE = \angle ABC

(corresponding angles)

\angle A

is common, so the triangles are similar (AA).

\mathstrut AB = 4 + 2

AB = 6

\dfrac{DE}{BC} = \dfrac{AD}{AB}

\mathstrut \dfrac{DE}{8} = \dfrac{4}{6}

DE = \dfrac{4}{6} \times 8

DE = 5.3333\ldots

\phantom{DE} = 5.33

cm (3 s.f.)

Question 5

Answer:

\phantom{DE} = 4.29

cm (3 s.f.)[3]

\angle ADE = \angle ABC

(corresponding angles)

\angle A

is common, so the triangles are similar (AA).

\mathstrut AB = 5 + 2

AB = 7

\dfrac{DE}{BC} = \dfrac{AD}{AB}

\mathstrut \dfrac{DE}{6} = \dfrac{5}{7}

DE = \dfrac{5}{7} \times 6

DE = 4.2857\ldots

\phantom{DE} = 4.29

cm (3 s.f.)

Question 6

(a)Answer:

x = 5

cm[2]

AB

matches

RQ

and

BC

matches

QP

\dfrac{BC}{QP} = \dfrac{AB}{RQ}

\mathstrut \dfrac{x}{10} = \dfrac{6}{12}

x = \dfrac{6}{12} \times 10

x = 5

(b)Answer:

\phantom{DB} = 2.67

cm (3 s.f.)[3]

\angle ADE = \angle ABC

(corresponding angles)

\angle A

is common, so the triangles are similar (AA).

\dfrac{AB}{AD} = \dfrac{BC}{DE}

\mathstrut \dfrac{AB}{4} = \dfrac{10}{6}

AB = \dfrac{10}{6} \times 4

AB = 6.6666\ldots

\mathstrut DB = 6.6666\ldots - 4

DB = 2.6666\ldots

\phantom{DB} = 2.67

cm (3 s.f.)

Question 7

(a)Answer:

x = 20

cm[2]

AB

matches

QP

and

BC

matches

PR

\dfrac{PR}{BC} = \dfrac{QP}{AB}

\mathstrut \dfrac{x}{10} = \dfrac{12}{6}

x = \dfrac{12}{6} \times 10

x = 20

(b)Answer:

DE = 9.6

cm[3]

\angle ADE = \angle ABC

(corresponding angles)

\angle A

is common, so the triangles are similar (AA).

\mathstrut AB = 8 + 2

AB = 10

\dfrac{DE}{BC} = \dfrac{AD}{AB}

\mathstrut \dfrac{DE}{12} = \dfrac{8}{10}

DE = \dfrac{8}{10} \times 12

DE = 9.6

Question 8

(a)Answer:

x = 8

cm[2]

BC

matches

RP

and

CA

matches

PQ

\dfrac{CA}{PQ} = \dfrac{BC}{RP}

\mathstrut \dfrac{x}{4} = \dfrac{7}{3.5}

x = \dfrac{7}{3.5} \times 4

x = 8

(b)Answer:

\phantom{DE} = 5.82

cm (3 s.f.)[3]

\angle ADE = \angle ABC

(corresponding angles)

\angle A

is common, so the triangles are similar (AA).

\mathstrut AB = 8 + 3

AB = 11

\dfrac{DE}{BC} = \dfrac{AD}{AB}

\mathstrut \dfrac{DE}{8} = \dfrac{8}{11}

DE = \dfrac{8}{11} \times 8

DE = 5.8181\ldots

\phantom{DE} = 5.82

cm (3 s.f.)

Sec 2 G1 Maths Congruence and similarity 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.

Answers and worked solutions

Question 1

Answer:

DE = 6.25

cm[3]

\angle ADE = \angle ABC

(corresponding angles)

\angle A

is common, so the triangles are similar (AA).

\mathstrut AB = 5 + 3

AB = 8

\dfrac{DE}{BC} = \dfrac{AD}{AB}

\mathstrut \dfrac{DE}{10} = \dfrac{5}{8}

DE = \dfrac{5}{8} \times 10

DE = 6.25

Question 2

Answer:

\phantom{DE} = 6.67

cm (3 s.f.)[3]

\angle ADE = \angle ABC

(corresponding angles)

\angle A

is common, so the triangles are similar (AA).

\mathstrut AB = 5 + 4

AB = 9

\dfrac{DE}{BC} = \dfrac{AD}{AB}

\mathstrut \dfrac{DE}{12} = \dfrac{5}{9}

DE = \dfrac{5}{9} \times 12

DE = 6.6666\ldots

\phantom{DE} = 6.67

cm (3 s.f.)

Question 3

Answer:

\phantom{DE} = 5.45

cm (3 s.f.)[3]

\angle ADE = \angle ABC

(corresponding angles)

\angle A

is common, so the triangles are similar (AA).

\mathstrut AB = 5 + 6

AB = 11

\dfrac{DE}{BC} = \dfrac{AD}{AB}

\mathstrut \dfrac{DE}{12} = \dfrac{5}{11}

DE = \dfrac{5}{11} \times 12

DE = 5.4545\ldots

\phantom{DE} = 5.45

cm (3 s.f.)

Question 4

Answer:

\phantom{DE} = 5.33

cm (3 s.f.)[3]

\angle ADE = \angle ABC

(corresponding angles)

\angle A

is common, so the triangles are similar (AA).

\mathstrut AB = 4 + 2

AB = 6

\dfrac{DE}{BC} = \dfrac{AD}{AB}

\mathstrut \dfrac{DE}{8} = \dfrac{4}{6}

DE = \dfrac{4}{6} \times 8

DE = 5.3333\ldots

\phantom{DE} = 5.33

cm (3 s.f.)

Question 5

Answer:

\phantom{DE} = 4.29

cm (3 s.f.)[3]

\angle ADE = \angle ABC

(corresponding angles)

\angle A

is common, so the triangles are similar (AA).

\mathstrut AB = 5 + 2

AB = 7

\dfrac{DE}{BC} = \dfrac{AD}{AB}

\mathstrut \dfrac{DE}{6} = \dfrac{5}{7}

DE = \dfrac{5}{7} \times 6

DE = 4.2857\ldots

\phantom{DE} = 4.29

cm (3 s.f.)

Question 6

(a)Answer:

x = 5

cm[2]

AB

matches

RQ

and

BC

matches

QP

\dfrac{BC}{QP} = \dfrac{AB}{RQ}

\mathstrut \dfrac{x}{10} = \dfrac{6}{12}

x = \dfrac{6}{12} \times 10

x = 5

(b)Answer:

\phantom{DB} = 2.67

cm (3 s.f.)[3]

\angle ADE = \angle ABC

(corresponding angles)

\angle A

is common, so the triangles are similar (AA).

\dfrac{AB}{AD} = \dfrac{BC}{DE}

\mathstrut \dfrac{AB}{4} = \dfrac{10}{6}

AB = \dfrac{10}{6} \times 4

AB = 6.6666\ldots

\mathstrut DB = 6.6666\ldots - 4

DB = 2.6666\ldots

\phantom{DB} = 2.67

cm (3 s.f.)

Question 7

(a)Answer:

x = 20

cm[2]

AB

matches

QP

and

BC

matches

PR

\dfrac{PR}{BC} = \dfrac{QP}{AB}

\mathstrut \dfrac{x}{10} = \dfrac{12}{6}

x = \dfrac{12}{6} \times 10

x = 20

(b)Answer:

DE = 9.6

cm[3]

\angle ADE = \angle ABC

(corresponding angles)

\angle A

is common, so the triangles are similar (AA).

\mathstrut AB = 8 + 2

AB = 10

\dfrac{DE}{BC} = \dfrac{AD}{AB}

\mathstrut \dfrac{DE}{12} = \dfrac{8}{10}

DE = \dfrac{8}{10} \times 12

DE = 9.6

Question 8

(a)Answer:

x = 8

cm[2]

BC

matches

RP

and

CA

matches

PQ

\dfrac{CA}{PQ} = \dfrac{BC}{RP}

\mathstrut \dfrac{x}{4} = \dfrac{7}{3.5}

x = \dfrac{7}{3.5} \times 4

x = 8

(b)Answer:

\phantom{DE} = 5.82

cm (3 s.f.)[3]

\angle ADE = \angle ABC

(corresponding angles)

\angle A

is common, so the triangles are similar (AA).

\mathstrut AB = 8 + 3

AB = 11

\dfrac{DE}{BC} = \dfrac{AD}{AB}

\mathstrut \dfrac{DE}{8} = \dfrac{8}{11}

DE = \dfrac{8}{11} \times 8

DE = 5.8181\ldots

\phantom{DE} = 5.82

cm (3 s.f.)