IM 8.2.7 Lesson: Similar Polygons
Choose whether each of the statements is true in all cases, in some cases, or in no cases.
If two figures are congruent, then they are similar.
If two figures are similar, then they are congruent.
If an angle is dilated with the center of dilation at its vertex, the angle measure may change.
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.
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 and using a scale factor of 2 and and 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.
Points through are translated to the right to create points through . All of the following are rectangles: , , , and . Which is greater, the area of blue rectangle DFCE or the total area of yellow rectangles and ?
Pair polygons that are similar to one another.
Explain how you know a pair of polygons is similar.
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
What’s the fewest number of pieces you can use? The most?