Similar Polygons


Exploring Similarity in Polygons.

(A). Let’s look at a square and a rhombus.

Priya says, “These polygons are similar because their side lengths are all the same.”
Clare says, “These polygons are not similar because the angles are different.”
Do you agree with either Priya or Clare? Explain your reasoning.

(B). Now, let’s look at rectangles ABCD and EFGH.

Jada says, “These rectangles are similar because all of the side lengths differ by 2.”
Lin says, “These rectangles are similar. I can dilate  AD  and  BC using a scale factor of 2 and  AB  and  CD  using a scale factor of 1.5 to make the rectangles congruent. Then I can use a translation to line up the rectangles.”
Do you agree with either Jada or Lin? Explain your reasoning.

(C). Draw two polygons that are similar but could be mistaken for not being similar.

Explain why the two polygons you drew are similar.

(D). Draw two polygons that are not similar but could be mistaken for being similar.


Sorting Similar Polygons.

Pair polygons that are similar to one another.


Creating Similar Triangles from a Triangle.

On the left is an equilateral triangle where dashed lines have been added, showing how you can partition an equilateral triangle into smaller similar triangles. Find a way to do this for the figure on the right, partitioning it into smaller figures which are similar to the figure.

(1). What’s the fewest number of pieces you can use?

(2). What’s the the most number of pieces you can use?


The two triangles are similar. Find side lengths a and b. Note: the two figures are not drawn to scale.


Jada claims that B’C’D’ is a dilation of BCD using A as the center of dilation.

What are some ways you can convince Jada that her claim is not true? (You can use the applet above to help you)


Choose whether each of the statements is true in all cases, in some cases, or in no cases.