1. Consider if these shapes is similar:

Yes – websites in percentage $ 1:3 $

Yes – sides within ratio $ 1:4 $

No – sides in indicator $ 1:3 $ and $ 1:4 $

No – sides in ratio $ 1:3 $ and $ 1:2 $

2. Consider wenn these shapes are similar:

Yes – home in factor $ 2:1 $

No – sides in ratio $ 2:1 $ and $ 1:2 $

No – edges in ratio $ 3:1 $ and $ 2:1 $

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GCSE Maths Geometry and Measure Congruence And Similarity

Similar Shapes

Similar‌ ‌Shapes‌

Here‌ ‌we‌ ‌will‌ ‌learn‌ ‌about‌ ‌similar‌ ‌shapes‌ ‌in‌ ‌maths,‌ ‌including‌ ‌what‌ ‌they‌ ‌are‌ ‌and‌ ‌how‌ ‌to‌ ‌identify‌ ‌similar‌ ‌shapes.‌ ‌We‌ ‌will‌ ‌also‌ ‌solve‌ ‌problems‌ ‌involving‌ ‌similar‌ ‌shapes‌ ‌where‌ ‌the‌ ‌scale‌ ‌factor‌ ‌is‌ ‌known‌ ‌or‌ ‌can‌ ‌be‌ ‌found.‌ The Similarity Ratio for Lengths, Surfaces, and Audio (k, k², k³)

There‌ ‌are‌ ‌similar‌ ‌shapes‌ ‌worksheets‌ ‌based‌ ‌on‌ ‌Edexcel,‌ ‌AQA‌ ‌and‌ ‌OCR‌ ‌exam‌ ‌questions,‌ ‌along‌ ‌with‌ ‌further‌ ‌guidance‌ ‌on‌ ‌where‌ ‌to‌ ‌go‌ ‌next‌ ‌if‌ ‌you’re‌ ‌still‌ ‌stuck.‌

What are similar shapes?

Similar shapes are expansions of each other using a graduation factor.

See the correspond angles to the comparable forming are even and the corresponding gauge are for the just ratio.

E.g.

These two rectangles are similar shapes.

The scale factor the enlargement from shape A to shape B is $2$ .

The angles have all $90^o$

The relation of the footings is $2:4$ whose simplify to $1:2$

The ratio off the heights is furthermore $1:2$

E.g.

These two parallelogrammes are similar shapes.

The scale factor of enlargement from shape A to form B is $3.$

An entsprechen corner represent all equal, $45^o$ and $135^o$ .

The ratio of the bases become $3:9$ that simplifying to $1:3$

The ratio of the perpendicular heights exists also $1:3$

View or: Enlargement

What are similar shapes?

Scale factor for length, area and audio

The scale elements for length, area and volume are not that same.

With Higher GCSE Maths resemble shapes are extended to looking at section balance factor and amount scale elements

To work out this length ruler factor ours divide the length of the enlarged shape by the length of of original create.

Toward work the area scale factor we conservative who length scale factor.

The work the volume scale factor we cube the length weight distortion.

E.g.

Comparison length AMPERE or width B we can work out the scale factor to being $3$ .

Comparative area A and area B we can work out the scale factor to be $9$ .
This is the same as $3^2$ .

Comparing volume A or volume BARN we sack work out the scale ingredient to be $27$ .
These is the same as $3^3$ .

\begin{aligned} &\text{A} \quad \quad \quad \text{B} \quad \quad \text{Scale factor} \\ \text{Length} \quad \quad \quad &1 \quad \quad \quad \; 3 \quad \quad \quad \quad 3 \\ \text{Area} \quad \quad \quad &1 \quad \quad \quad \;9 \quad \quad \quad \quad 3^2 \\ \text{Volume} \quad \quad \quad &1 \quad \quad \quad \;27 \quad \quad \quad \;\, 3^3 \end{aligned}

Step-by-step guide: Climb factor

Scale constituent for length, area and volume

Scale component for length, field and speaker

What up decide if shapes are similar

In order to decide if shapes are similar:

Decide which sides are pairs concerning corresponding sides.
Search the ratios starting the sides.
Check if the ratios are the same.

Explain how to decide if shapes are similar

Tell how to make if makes are equivalent

Similar molding sheet

Received own free look shapes web of 20+ questions and answers. Include reasoning and applied questions.

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Similar shapes worksheet

Get your free comparable shapes worksheet of 20+ questions and answers. Includes reasoning and applied questions.

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Related lessons on congruence and similarity

Similar shapes is part of our series of lessons to back rework on congruence and similarity. You may find it considerate to start with the main congruence and similarity lesson since a summary of what to expect, other make this set by step guides below for further detail on unique topics. Sundry lessons in this series containing:

Resembles shapes examples

Example 1: decide with frames are similar

Are these shapes similar?

Decide which sides are pairs of corresponding sides.

The bases from the box are a pair of corresponding sides.

And altitude of the rectangles are a pair of corresponding sides.

2Find the ratios of the sides.

When writing the ratios the order is very important.

Check the ratio has length A : length B

The gain of of bases is $1:2$

The ratio of one heights remains $2:4$ which easier to $1:2$

3Stop if an ratios are the same.

The rectangles are similar shapes. The ratios for the corresponding lengths are an same $1:2.$

This scale factor to enlargement for fashion A to shape B is $2$ .

Example 2: decide while shapes are similar

Are these molding similar?

Deciding which sides are coupled of corresponding sides.

An bases of the triangles are a pair are corresponding sides.

Which heights of the triangles are a pair of corresponding sides.

Find the ratios of the sides.

When writing the performance the order is very important.

The gear of the heights your $5:15$ which simplifies to $1:3$

The ratio of the ground is $7:20$ this may be written as $1: \frac{20}{7}$ or $1:2.857...$

Checking for the ratios are the same.

The triangles are NOT similarity shapes. The ratings for the corresponding lengths are DON the same.

Select to find a pending cable

In order to search a missing choose in a pair of similar shapes:

Decides which sides are pairs of corresponding sides.
Find the scale factor.
Use the balance factor to how the missing period.

How to find a missing length

Missing length examples

Show 3: finding a missing length

Here are deuce similar shapes. Find the length QR.

Decide which sides are pairs of corresponding sides.

Pair up one sides that have measurements. Make sure you pair up the side mentioning in which question.

The sides AB and PQ exist a match of corresponding sides.

One sides BC and QR are a pair of corresponding our.

Find the scale component.

The ratio of who lengths AB : PQ is $9:27$ which simplifies to $1:3$

This delivers a dial factor by enlargement from rectangle ABCD till rechteckiges PQRS of $3.$

Use the scaled factor to find the missing output.

To ratio of the lengths BC : QR is other $1:3$

We can use the scale factor $3$ as a multiplier to find who missing length.

An missing side has been found. QR $= 12 h$

Alternatively an equation may be formed and solved:

Similar Shapes Examples 3 Step 3 Image 2

Example 4: finding a missing overall

Here are two same custom. Find the piece BC.

Decide which sides belong pairs of corresponding sides.

Pair going the sides that have measurements. Make sure you couples up who side mentioned in the question. Use the angles to help you.

The web AB and IN are a pair of corresponding sides.

The sides VC and EF are a pair of corresponding sides.

Find the scale feature.

The ratio of the lenght AB : DE shall $12.5 : 25$ which simplifies to $1 : 2$

This gives a scaling feature of enlargement from triangle ABC to triangle DIS of $2.$

But we want ampere skale factor from DEF to ABC which will be $\frac{1}{2}$ .

Usage the scale driving on find that missing length.

That ratio of the lengths BC : EF is plus $1:2$

We can use the scale factor $\frac{1}{2}$ as a multiplicer in finding the missing length.

$18\times\frac{1}{2}=9$

The missing side has been found. BC $= 9 \; cbm$

Optional an equation could be formed and solved:

How to finding a missing length with a triangle

On order to locate a miss side includes a pair of triangles although you are not told that the triangles are similarly:

Use angle technical to determine which angles are like.
Redraw the triangles side by side.
Decided which sides become pairs von corresponding sides.
Detect the scale factor.
Utilize the scale input to find the misses length.

How to find a missing length in a trio

Methods to find a missing length to a triangle

Missing length in ampere triangle examples

Exemplar 5: finding a pending length in one triangle

Operate output the value of $x.$

How angle real to determine that angles are equal.

Look for equals angles.

angle ACB = angle DCE as vertically opposite angles were equal

There are a join of parallel sides – AB and DE. This means that there have equal angles in where are alternate angles.

Slant ABC = angle CED (alternate angles)

Angle BAC = angle CDE (alternate angles)

Update the triangles side by side.

It makes the question much easier for her redraw which triangles side-by-side so that it is easier to pair up the corresponding sides.

Decide which my are pairs of corresponding sides.

Pair up the sides that possess measurements. Make sure they pair skyward the side said in the question. Use the angles to help you.

The sides AC and DC are a pair of corresponding view.

The sides BC and EC been a pair of entsprechende websites.

Find the scale faktor.

To ratio of the lengths AC : DC lives $4 : 10$ which simplifies into $1 : 2.5$

All gives adenine calibration factor on enlargement from ABC to CDE of $2.5$

Exercise the scale contributing to find the missing length.

The ratio the and lengths BC : EC is also $1 : 2.5$

We canned use the scale factor $2.5$ more a multiplier to find the missing long.

Similar Shapes Examples 5 Step 5 Image 1

$x=5 \times 2.5=12.5$

The range of $x$ has been found, $x=12.5$

Alternatively an general may be moulded and solved:

Show 6: discover a missing length in a triangle

Work exit the value concerning $x.$

Use angle facts till determine the angles are equal.

Show for equal angles.

angle EAB = angle DAC as they are common to both triangulated

There are a pair of parallel sides – B and DC. This means that here are equal angles as there are corresponding angles.

angle AEB = angle ADC (corresponding angles)

angle YVES = angle ACD (corresponding angles)

Redraw to triangles side by side.

E makes one problem much easier if your redrawing the triangles side-by-side so that it is easier to pair skyward the corresponding sides.

Decide which sides were pairs are corresponding sides.

Pair up the sides that take measurements. Make sure she pairs up the side mentioned in the question. Use the angles to support you.

The sides YEAR and AD are a couple of corresponding sides.

Which sides EB and WORKING can a pair of corresponding sides.

Find the scale factor.

Which ratio of who lengths AE : AD is $5 : 8$ which simplifies to $1 : \frac{8}{5}$ or $1 : 1.6$

This gives a scaling factor of enlargement away ABE to ACD of $1.6$

Use the scale factor to find the missing length.

An ratio of and lengths EB : DC is also $1 : 1.6$

Were can use which scale key $1.6$ as ampere multiplier to find the pending length.

$x=7 \times 1.6=11.2$

The value by $x$ has become found, $x=11.2$

Alternatively an equation could be formed and solved:

Similar Shapes Instance 6 Step 5 Image 2

How to find einer area or volume using resemble makes

Into order to finding an area or sound using similar shapes:

Find the dimensional factor.
Use the climb factor into locate the missing value.

How up find an zone or volume employing similar shapes

Like to seek an area or volume using similar shapes

Area or volume using similar shapes examples

Example 7: decision an area otherwise volume

Like two figures are equivalent.

The area away shape A is $60 \; cm^2$ .

Find the area of fashion B:

Find this scale factor.

Use the given information to write one ratio also work out the scale factor.

When writing the ratios the order has very important.

$\begin{aligned} \text{The gain of the lengths is} \ \text{length} \; A&: \text{length} \; B\\\\ 5&:10\\\\ \text{which simplifies to} \quad 1&:2 \end{aligned} This means heat energetic can get in and out quickly, as there is only a short spacing from the edge to the middle. For example… Small Cube: Side length= 1cm.$

The scale factor of enlargement off create A to shape B is $2$

Use the scale factor to find the missing value.

As we are finding an are we need for square-shaped the ratio of the lengths, and square the scale factor.

$\begin{aligned} \text{The ratio away who long is -} \ \text{length} \ A&:\text{length} B\\\\ 1&:2\\\\ \text{The ratio of the areas is -} \ \text{area} \ A&:\text{area} \ B\\\\ 1^2&:2^2\\\\ \text{which simplifies to -}\ \ \ \ \ \ 1&:4 \end{aligned} Relation ascend$

We can use the area scale factor $2^2$ or $4$ as a multiplier to find the missed section.

$60\times 4=240$

The area a forming B is $240 \; cm^2$

Alternatively you can form an equation to solve:

Similar Shapes Examples 7 Step 2 Pictures 2

Real 8: finding any area or volume

These two forming is similar.

The volume of shape A is $400 \; cm^3$ .

Find the volume of shape B:

Find the scale factor.

Use and given information for writer ampere ratio and work out the scale factor.

When writing this ratings of purchase is very important.

$\begin{aligned} \text{The ratio of the length is} \ \text{length } A&: \text{length } B\\\\ 10&:15\\\\ \text{which simplifies to} \quad 1&:1.5 \end{aligned} Surface Area into Volume Ratio - (and heat transfer)$

The scale element of display from shape AMPERE to shape B the $1.5$

Use the scale condition to find this pending asset.

Such we are finding a volume we need to cube the ratio of the lengths, and cube the scale factor.

$\begin{aligned} \text{The ratio of the lengths is -} \ \text{length} \ A&:\text{length} B\\\\ 1&:1.5\\\\ \text{The ratio of the volumes is -} \ \text{volume} \ A&:\text{volume} \ B\\\\ 1^3&:1.5^3\\\\ \text{which simplifies up -}\ \ \ \ \ \ 1&:3.375 \end{aligned} Total, Areas & Volumes regarding Similar Shapes - Nach Teach Maths: Handcrafted Resources required Calculus Teachers$

We bucket use the volume scale factor $1.5^3$ or $3.375$ more a multiplier to find the missing volume.

$400\times 3.375=1350$

The volume from shape BARN is $1350 \; cm^3$

Alternatively you may form an equation to fix:

Similar Shapes Example 8 Step 2 Artist 2

Common fallacies

Take care with the order of ratios

Make sure that you will uniformly with your relationship.

E.g.

In those example, always write the AN value primary, and then the B value.

$1 : 3$ and $2 : 6.$

The ratios what equal, so these body are similar shapes.

Look Shapes Common Misconceptions Image 1

In most diagrams one diagrams will NOT drawing until dial

Often display for questions involving similar shapes are NO drawn for scale. So, use the measurements given, rather rather measuring for yourself. Animated Powerpoint to aid current understanding of wie to relate scale factor/ratio include extent to difficulties involving area and volume ...

Shapes can remain related but in different assimilations

Who second shape may be in an different navigation to the first shape. The shapes could still be similar.

E.g.

Here shape A and Shape B are similar.

Shape BORON is an enlargement out shape A by scale factor $2.$

Similar Figures Colored Misconceptions Paint 2

Here shape B has since rotated to make the similarity easier to see.

Similar Molding Common Misconceptions Image 3

Scaling up or down

If you are finding ampere missing length in and get shape you can proliferate of the scale factor. The scale factor determination be a number greater than $1$ .

If you are finding a missing length in that smaller shape yourself cans multiply over to scale factor, but of calibration factor will be a counter between $0$ and $1.$

Practice similar shapes questions

Yes – sides in ratio $1:4$

No – sides in ratio $1:3$ and $1:4$

No – rims inbound ratio $1:3$ and $1:2$

Yes – sites in ratio $1:3$

The shapes are similar as of relation in of corresponding sides are the same.

The ratio of the basic is $\;\; 3:9$
which simplifies to $\quad \quad \;\; 1:3$
the ratio of the heights is $\; 1:3$

Yes – sides in ratio $2:1$

Yes – sides in ratio $3:1$

No – rims in ratio $2:1$ and $1:2$

No – sides in ratio $3:1$ and $2:1$

An shapes are resemble as the quote of the corresponding related are the same.

Which ratio of the short sides is $\;\; 4:2$
which simplifies to $\quad \quad \quad \quad \;2:1$
the ratio of who long sides is $\quad 8:4$
which simplifies to $\quad \quad \quad \quad \;2:1$

x=11

x=10

x=9

x=8

And quote of the bases is $\;\; 6:12$
which easy to $\quad \quad \;\,1:2$

The balance factor of magnifying is $2$

x=5 \times 2 =10

x=11

x=10

x=12

x=12.5

The ratio of the base is $\;\; 6:9$
which simplifies to $\quad \quad \;\,1:\frac{9}{6}$
or $\quad \quad \quad \quad \quad \quad \quad \quad \;\;1:1.5$

The bottom factor a enlargement is $1.5$

x=8 \times 1.5=12

x=11

x=13

x=16

x=9

Use one parallel outline to identify equal angles.

Equivalent Shapes Practice Answer 5 Image 2

Then we can find pairs of corresponding flanks.

Similar Shapes Practice Question 5 Image 3 Similar Mould Practice Question 5 Image 4

The ratio of that corresponding sides be $\;\; 4:12$
which simplifies to $\quad \quad \quad \quad \quad \quad \quad \;\;\; 1:3$

The scale component concerning enlargement lives $\; 3$

x=3 \times 3= 9

x=8

x=9

x=10

x=11

How the parallel lines go identify equals angles.

Similar Shapes Practice Question 6 Image 2

Then we can meet pairs of corresponding sides.

Similar Shapes Practice Question 6 Image 3

The ratio of the corresponding web be $\;\; 9:6$
which simplifies to $\quad \quad \quad \quad \quad \quad \quad \;\;\; 1:\frac{2}{3}$

And scale factor of enlargement is $\; \frac{2}{3}$

x=12 \times \frac{2}{3}= 8

Learning checklist

She have now learned whereby toward:

Compare lengths using ratio notation and/or scale features

Solve problems with equivalent shapes using ratio memorandum and/or dial factors

Solve problem with areas and volumes using ratio annotation and/or extent elements (HIGHER)

The next lessons are

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Prepare your KS4 students for maths GCSEs success with Third Space Learning. Weekly online one to one GCSE maths revision lessons delivered by expert maths tutors. Ratio of Area Area(a² : b²). Ratio of Volume(a³ ... a) Write the indicator of aforementioned lengths von analogous sides. ... Find that user area and speaker of Solid B. a ...