Similarity and Congruence

1. Measure these two lines, what is the scale factor?

These two triangles are similar. Triangle B is twice the size of triangle A. Write down the corresponding lengths and angles of triangle B.

2. Fill in the missing lengths for these similar triangles(Hint, you will need to find the scale factor in the same way as question 1)

These two triangles are similar. Find the scale factor.

Word Box

Corresponding: Two or more things that match in some way. For example, two angles correspond to each other if they are in the same place in either triangle.

Scale Factor: The amount of times that one number is increased or decreased by another. For example, 6 is twice as large as 3. Therefore if 3 is increased by a scale factor of 2, it becomes 6.

Explain: Give some reasons for the answer you give.

6cm

4cm 5cm

85° 45 °

50°

AB

12cm

5cm

9cm

3cm

9mm

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Answer……………………………

3.

Diagram NOT accurately drawn

In the diagram, AB = BC = CD = DA.

Prove that triangle ADB is congruent to triangle CDB.

(Total 3 marks)

6.

Diagram NOT accurately drawn

5.6cm

8mm

6.3cm

3.5cm

5mm

B

A C

D

ABC is an equilateral triangle.D lies on BC.AD is perpendicular to BC.

(a) Prove that triangle ADC is congruent to triangle ADB.

(3)

(b) Hence, prove that BD = 21

AB.(2)

(Total 5 marks)

7.

Diagram NOT accurately drawn

ABC is an equilateral triangle.D lies on BC.AD is perpendicular to BC.

Prove that triangle ADC is congruent to triangle ADB.

(Total 3 marks)

A

B D C

A

B D C

Extension 1

Extension 21.

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