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In this lesson, we will learn how to use the properties of similar polygons to find unknown angles, side lengths, scale factors, and perimeters.

Q1:

If the two following polygons are similar, find the value of π₯ .

Q2:

If π΄ π΅ πΆ π· πΈ βΌ π π π π π , find the scale factor of π΄ π΅ πΆ π· πΈ to π π π π π and the perimeter of π π π π π .

Q3:

If two triangles are similar, then their corresponding angles are .

Q4:

If β³ π΄ π΅ πΆ βΌ β³ π π π , find the lengths of π΅ πΆ and π π .

Q5:

Find π β πΆ + π β π· + π β πΈ .

Q6:

Are these two polygons similar? If yes, find the scale factor from π π π πΏ to π΄ π΅ πΆ π· .

Q7:

Are the two polygons similar?

Q8:

If π΅ πΊ πΆ π· βΌ πΏ π π π , then π΅ πΊ πΆ π· = β¦ π π .

Q9:

Given that π΄ π΅ πΆ π· βΌ πΈ πΉ πΊ π» , determine the length of πΊ π» .

Q10:

Given that π΄ π΅ πΆ π· βΌ π π π πΏ , find π β π πΏ π and the length of πΆ π· .

Q11:

If π β π΅ + π β πΆ = 1 4 5 β , find π β π .

Q12:

If β³ π π π βΌ β³ π΄ π΅ πΆ , π β π = 2 6 β , and π β πΆ = 6 6 β , find π β π .

Q13:

A college professor was using a projector to give his lectures. A slide whose dimensions are 11 inches wide and 7 inches high was projected into an image that was 5 3 1 2 inches wide. Find the height of the projected image.

Q14:

Given that the rectangle π΄ π΅ πΆ π· is similar to the rectangle π π΅ π π , find the length of π π .

Q15:

A rectangle that is 15 by 10 is similar to a second rectangle with perimeter 40. Find the length and the area of the second rectangle.

Q16:

The image of a shape has a perimeter of 40 following a dilation by a scale factor of 1 2 . What would the perimeter of the original shape be?

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