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In this lesson, we will learn how to use proportions in order to identify similar polygons.

Q1:

Are the two polygons similar?

Q2:

Given that the triangles shown are similar, determine π₯ .

Q3:

Is the polygon π΄ π΅ πΆ π· similar to the polygon πΈ πΉ πΊ π» ?

Q4:

Which of the following statements correctly defines similarity for polygons?

Q5:

Find the lengths of π΄ π΅ and π΄ πΆ rounded to the nearest tenth.

Q6:

π΄ π΅ πΆ π· βΌ π π π πΏ and the perimeter of π΄ π΅ πΆ π· = 1 7 7 c m . Calculate the scale factor of similarity of π π π πΏ to π΄ π΅ πΆ π· and the perimeter of π π π πΏ .

Q7:

The ratio between corresponding sides of two similar triangles is 1 0 βΆ 9 . If the length of the base of the larger triangle is 19.7, find the length of the base of the smaller triangle rounding the answer to the nearest tenth.

Q8:

The ratio between the areas of two similar polygons is 1 βΆ 4 . Given that the length of one side of the smaller one is 8 cm, calculate the length of the corresponding side of the bigger one.

Q9:

In the figure, given that the two triangles are similar, work out the value of π₯ .

Q10:

Q11:

If the corresponding angles in two triangles are equal, then the two triangles .

Q12:

If the scale factor of two similar polygons equals 1, what can you say about the polygons?

Q13:

A polygon has sides 2, 4, 3, 8, and 4. A second similar polygon has perimeter 31.5. What are its sides?

Q14:

If polygon π΄ and polygon π΅ are both similar to a third polygon, then polygons π΄ and π΅ are .

Q15:

Consider two similar polygons π΄ π΅ πΆ π· and π π π πΏ . Which angle in π΄ π΅ πΆ π· corresponds to β π ?

Q16:

Is rectangle π΄ π΅ πΆ π· similar to rectangle π π π πΏ ?

Q17:

Any two triangles are similar when their corresponding are proportional.

Q18:

If the polygon π 1 is similar to the polygon π 2 and the scale factor from π 1 to π 2 is positive and less than 1, then π 1 is π 2 .

Q19:

Consider the points π΄ ( 3 , 5 ) , π΅ ( 3 , β 5 ) , πΆ ( 5 , β 5 ) , π· ( 5 , 5 ) , π ( β 3 , 8 ) , π ( β 3 , 2 8 ) , π ( 1 , 2 8 ) , and π ( 1 , 8 ) . Is the rectangle π΄ π΅ πΆ π· similar to the rectangle π π π π ?

Q20:

Are these two triangles similar?

Q21:

Are these two polygons similar?

Q22:

Is polygon π΄ π΅ πΆ π· similar to polygon πΊ πΉ πΈ π ?

Q23:

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

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