Similarity Practice Problems

Which statement provides a valid justification for why all circles are similar?

• All circles have the same shape - a circle - so they must be similar

• All circles have no angles and no sides, so they must be similar

• I can translate any circle exactly onto another, so they must be similar

• I can translate the center of any circle to the center of another, and then dilate from that center by an appropriate scale factor, so they must be similar

Similar or not?

• Similar

• Not similar

Answer explanation

These triangles are not similar because the sides are not equally scaled

Similar or not?

• Similar

• Not similar

Answer explanation

While these shapes have the same sides, the angles are not same

Similar or not?

• Similar

• Not similar

Answer explanation

These figures are similar because the sides have all been scaled equally and the angles didn't change from one figure to the other

Similar or not?

• Similar

• Not similar

Answer explanation

The sides were not scaled equally

Select ALL sequences of transformations that would show that

 $\Delta ABC$   and  $\Delta AED$   are similar. The length of AC is 6 units.

• Dilate triangle ABC using center A by a scale factor of 1/2, then reflect over line AC

• Dilate triangle AED using center A by scale factor if 2, then reflect over line AC

• Reflect triangle ABC over line AC, then dilate using center A by a scale factor of 1/2

• Reflect triangle AED over line AC, then dilate using center A by a scale factor of 2

• Translate triangle AED by directed line segment DC, then dilate using center C by scale factor 2

True or false?

Two equilateral triangles are similar

• True

• False

Answer explanation

Must be true. Dilate the first triangle using any center by a scale factor that is the ratio of the length of sides of the second triangle to the length of the sides of the first. Then apply the Angle-Side-Angle Triangle Congruence Theorem

True or false?

An equilateral triangle and a square are similar

• True

• False

Answer explanation

Definitely can't be true. Rigid motions and dilations both take line segment to line segments, so the image of a polygon must have the same number of sides.

Select ALL true statements given that angle AED is congruent to angle ABC

• $\angle ACB\ is\ 180-x\degree$

• $\angle ACB\ is\ x\degree$

• $\Delta ACB\ \sim\ \Delta ADE$

• $AD\ =\ \frac{1}{3}AC$

• $AD=\frac{1}{2}DC$