More similarity.pptx

EDEXCEL GCSE MATHS · HIGHER

More similarity

Similarity and congruence

Lesson 4 of 5

openrevise.com

EDEXCEL GCSE MATHS · HIGHER

Warm-up

Similarity and congruence

Lesson 4 of 5

Answer each one, then check.

1

What is the scale factor from 6 to 9?

2

Work out 1.5².

3

What do corresponding angles on parallel lines do?

4

Work out √(27/12).

5

If k = 3, what is k²?

openrevise.com

EDEXCEL GCSE MATHS · HIGHER

Warm-up - Answers

Similarity and congruence

Lesson 4 of 5

1

What is the scale factor from 6 to 9?

1.5

2

Work out 1.5².

2.25

3

What do corresponding angles on parallel lines do?

They are equal

4

Work out √(27/12).

1.5

5

If k = 3, what is k²?

9

openrevise.com

EDEXCEL GCSE MATHS · HIGHER

Learning Objectives

Similarity and congruence

Lesson 4 of 5

1

Find similar triangles created by parallel lines.

2

Find missing lengths using scale factors.

3

Use the area scale factor k².

4

Work backwards from an area ratio to a length ratio.

openrevise.com

EDEXCEL GCSE MATHS · HIGHER

A Triangle Cut by a Parallel Line

Similarity and congruence

Lesson 4 of 5

A line parallel to one side of a triangle makes a smaller similar triangle.

openrevise.com

EDEXCEL GCSE MATHS · HIGHER

Similarity and congruence

Lesson 4 of 5

PARALLEL LINES

If DE is parallel to BC, then triangle ADE is similar to triangle ABC.

The corresponding angles are equal, and the angle at A is common.

openrevise.com

EDEXCEL GCSE MATHS · HIGHER

Finding a Length

Similarity and congruence

Lesson 4 of 5

In triangle ABC, DE is parallel to BC. AD = 4 cm, DB = 2 cm and DE = 5 cm. Find BC.

1

AB = AD + DB

4 + 2 = 6

2

Scale factor from ADE to ABC

6/4 = 1.5

3

BC = DE × 1.5

5 × 1.5

ANSWER

BC = 7.5 cm

openrevise.com

EDEXCEL GCSE MATHS · HIGHER

Watch the Sides

Similarity and congruence

Lesson 4 of 5

The whole side, not just the piece, is the corresponding length.

Use AB, not DB

The similar triangles are ADE and ABC, so AD corresponds to AB.

Add the parts

AB = AD + DB.

Label the two triangles

Write them in matching order: ADE and ABC.

openrevise.com

EDEXCEL GCSE MATHS · HIGHER

Similarity and congruence

Lesson 4 of 5

AREA SCALE FACTOR

If two shapes are similar with length scale factor k, their areas are in the ratio 1 : k².

Doubling all lengths multiplies the area by 4; tripling multiplies it by 9.

openrevise.com

EDEXCEL GCSE MATHS · HIGHER

Finding an Area

Similarity and congruence

Lesson 4 of 5

Two similar rectangles have lengths 12 cm and 18 cm. The area of the smaller is 40 cm². Find the area of the larger.

1

Length scale factor

18/12 = 1.5

2

Area scale factor

1.5² = 2.25

3

Area of the larger

40 × 2.25

ANSWER

90 cm²

openrevise.com

EDEXCEL GCSE MATHS · HIGHER

From Areas to Lengths

Similarity and congruence

Lesson 4 of 5

Two similar triangles have areas 12 cm² and 27 cm². Find the ratio of their lengths in its simplest form.

1

Ratio of areas

12 : 27 = 4 : 9

2

Take the square root

√4 : √9 = 2 : 3

ANSWER

The ratio of the lengths is 2 : 3.

openrevise.com

EDEXCEL GCSE MATHS · HIGHER

Scale Factors

Similarity and congruence

Lesson 4 of 5

For similar shapes with length scale factor k.

Measure

Scale factor

Example, k = 3

Lengths

k

3

Areas

k²

9

Volumes

k³

27

openrevise.com

EDEXCEL GCSE MATHS · HIGHER

Key Terms

Similarity and congruence

Lesson 4 of 5

Similar triangles

Triangles with equal angles and proportional sides.

Scale factor

The multiplier for lengths.

Area scale factor

The square of the length scale factor.

Parallel

Lines that never meet.

Corresponding angles

Equal angles in matching positions on parallel lines.

Ratio

A comparison of two quantities.

openrevise.com

EDEXCEL GCSE MATHS · HIGHER

Similarity and congruence

Lesson 4 of 5

YOUR TASK

Shadows and Similar Triangles

12 minutes

A 1.5 m post casts a shadow of 2 m at the same time as a tree casts a shadow of 12 m. Draw two similar right-angled triangles and find the height of the tree. If the post's triangle has area 1.5 m², find the area of the tree's triangle.

1

Draw both triangles.

2

Find the length scale factor.

3

Square it for area.

WHAT A GOOD ANSWER SHOWS

Scale factor 12 ÷ 2 = 6, so the tree is 1.5 × 6 = 9 m tall. The area scale factor is 6² = 36, so the area is 1.5 × 36 = 54 m².

openrevise.com

EDEXCEL GCSE MATHS · HIGHER

Can I...?

Similarity and congruence

Lesson 4 of 5

Spot similar triangles from parallel lines.

Use the whole side, not part of it.

Find a missing length.

Use k² for areas.

Find an area from a length ratio.

Find a length ratio from an area ratio.

Write the ratio in simplest form.

Explain my reasoning.

openrevise.com

EDEXCEL GCSE MATHS · HIGHER

Summary & Exam Focus

A line parallel to a side makes a similar triangle.

Match corresponding sides in the same order.

Area scale factor = k².

Take a square root to go from area ratio to length ratio.

EXAM FOCUS

In triangle ABC, DE is parallel to BC. AD = 4 cm, DB = 2 cm and DE = 5 cm. Work out the length of BC. (3 marks)

The similar triangles are ADE and ABC. Use AB = AD + DB in the scale factor, not DB alone.

openrevise.com