Unit 8 Lesson 5: Definition of Similar Figures

Question 1

dilation

Answer 1

the act or process of expanding or reducing a shape by the same scale factor

Question 2

distance formula

Answer 2

a method of calculating the distance between points on the coordinate plane

Question 3

scale factor

Answer 3

a number representing the ratio between the dimension of an object and the dimension of a dilation of that object

Question 4

similar figures

Answer 4

two-dimensional figures of different sizes but the same shape

Question 5

translation

Answer 5

a transformation that changes the position of a point or shape

Question 6

AA Similarity Criterion

Answer 6

Also known as AA Similarity Postulate, this postulate shows that two sets of corresponding angles have the same measurement. A stands for “angles.”

Question 7

SSS Similarity Criterion

Answer 7

Also known as SSS Similarity Theorem, this method proves that various corresponding sides are proportional—not necessarily congruent as in determining congruence, but proportional. It demonstrates that all three sets of sides are proportional between the two triangles.

Question 8

SAS Similarity Criterion –

Answer 8

Also known as SAS Similarity Theorem, this method demonstrates that two sets of sides are proportional and the included angle measures the same in both figures.

Question 9

Why isn’t the AA criterion known as the AAA criterion?

Answer 9

Because if you know two of the angles in a triangle, you know the third; if two angles are identical in triangle ABC
and triangle A’B’C’
, the third angle must be the same in each triangle.

Question 10

What happens to the measure of the angles when a triangle is dilated?

Answer 10

They stay the same size.

Question 11

If a triangle is dilated using a scale factor other than 1, what happens to the lengths of the triangle’s sides?

Answer 11

All three sides increase or decrease using the same proportion.

Question 12

What is the only type of geometric transformation in which the size of a figure can change?

Answer 12

dilation

Question 13

Frankie draws a circle and increases its size through dilation. What can you conclude about the scale factor Frankie uses?

Answer 13

Frankie’s scale factor must be greater than 1.

Question 14

What is one way in which dilation is different from reflection?

Answer 14

Dilation changes the size of a figure, and reflection does not.

Question 15

Maria draws a triangle. She rotates the triangle, translates the triangle to the right, and dilates it using the scale factor of 3. If the height of the original triangle is 15 cm, what is the height of the transformed triangle?

Answer 15

The height of the transformed triangle is 45 cm.