Geometry | Unit 3 | Lesson 8: Are They All Similar? | Practice Problems

Explain which step is invalid and why in the invalid proof that all isosceles triangles are similar.

• Step 1: Draw 2 isosceles triangles ABC and DEF where AC=BC and DF=EF.

• Step 2: Dilate triangle ABC to a new triangle A’B’C using center C and scale factor DF/AC so that A’C=B’C=DF=EF.

• Step 3: Translate by directed line segment CF to take A’B’C to a new triangle A’’B’’F.

• Step 4: Rotate using center F to take A’’ to D since A’’F=DF.

• Step 5: Rotate using center F to take B’’ to E since B’’F=EF.

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.

Which pair of polygons is similar?

• 
• Option B

• Option C

• Option D

Select all sequences of transformations that would show that triangles ABC and AED are similar.

• 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 a scale factor of 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.

Determine if each statement must be true, could possibly be true, or definitely can't be true.

Find a sequence of rigid transformations and dilations that takes square EFGH to square ABCD.

Select all true statements given that angle AED is congruent to angle ABC.

• Angle ACB is 180-x degrees.

• Angle ACB is x degrees.

• Triangle ACB is similar to triangle ADE.

• AD = 1/3 AC.

• AD = 1/2 DC.