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In this lesson, we will learn how to use the properties of similar triangles to solve problems.

Q1:

These two rectangles are similar. Given that the area of the yellow one is 69.3 cm^{2}, find the area of the green rectangle.

Q2:

Given that π· πΈ = 7 4 m , πΈ π΅ = 3 2 m , and πΈ π΄ = 4 8 m , find the length of πΆ π΄ .

Q3:

In the given figure, π· πΈ and π΅ πΆ are parallel. Use similarity to work out the value of π₯ .

Q4:

If β³ π΄ π΅ πΆ βΌ β³ π΄ π· πΈ , evaluate π₯ .

Q5:

Given that β³ πΉ πΊ π» βΌ β³ π π π , if 6 units are added to the length of each side, are the new triangles similar?

Q6:

Find the value of π₯ .

Q7:

Which of the following properties is enough to conclude that two triangles are similar?

Q8:

Fill in the blank: β³ π΄ π΅ πΆ βΌ β³ βΌ β³ .

Q9:

Given that β³ π΄ π΅ πΆ and β³ π· πΈ πΉ are similar, find the length of π· π» .

Q10:

π π π is a right-angled triangle at π . πΏ is a point on π π such that οͺ π πΏ β π π . If π π = 1 9 c m and π π = 8 c m , calculate the lengths of π πΏ and π πΏ . Round your answers to the nearest hundredth.

Q11:

Triangles π΄ π΅ πΆ and π΄ π΅ πΆ β² β² β² are similar.

Work out the value of π₯ .

Work out the value of π¦ .

Q12:

Triangles π΄ π΅ πΆ and π΄ β² π΅ β² πΆ β² are similar.

Work out the length of π΄ πΆ .

Work out the length of π΅ β² πΆ β² .

Q13:

Triangle can be dilated by a scale factor of two onto triangle .

Determine the length of .

Find the size of angle .

Q14:

Triangles and are similar.

Work out the size of angle .

Work out the value of .

Q15:

Given that π π π πΏ is a square, π β π π π = ( π + 8 4 ) β , and π β π π π = ( π + 3 3 ) β , find π .

Q16:

Find the value of rounded to the nearest hundredth, if needed.

Q17:

Triangles π΄ π΅ πΆ and π΄ π· πΈ are similar. Find π₯ to the nearest integer.

Q18:

Given that π΄ π· π· πΆ = 3 7 and the area of β³ π΄ π΅ πΆ = 4 8 4 c m 2 , find the area of β³ π΄ π· πΈ .

Q19:

π΄ π΅ πΆ π· πΈ βΌ πΉ πΊ π» πΎ π where π΄ πΆ = 4 6 c m and πΉ π» = 1 1 . 5 c m . If the area of π΄ π΅ πΆ π· πΈ = 3 0 3 6 c m 2 , what is the area of πΉ πΊ π» πΎ π ?

Q20:

The diagonal of a small square is 3 4 of the length of the diagonal of a larger square. If the area of the smaller square is 9 cm^{2}, what is the area of the larger square?

Q21:

π΄ π΅ πΆ π· βΌ πΈ πΉ πΊ π» where π΄ π = 7 c m and πΈ π = 2 . 8 c m . If the area of π΄ π΅ πΆ π· is 1β848 cm^{2}, what is the area of πΈ πΉ πΊ π» ?

Q22:

If the ratio between the sides of two similar polygons is 7 βΆ 6 , what is the ratio between their areas?

Q23:

Square A is an enlargement of Square B by a scale factor of 2 3 . If the perimeter of Square A equals 56 cm, what is the area of Square B? Give your answer to the nearest hundredth.

Q24:

It cost 3 , 7 9 9 p o u n d s to fit wooden flooring in a class with dimensions 28 m and 10 m. How much would it cost to fit wooden flooring in a similar room with dimensions 84 m and 30 m.

Q25:

If π΄ π΅ πΆ π· βΌ πΈ πΉ πΊ π» , find the scale factor of similarity of πΈ πΉ πΊ π» to π΄ π΅ πΆ π· and the values of π and π .

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