Chapter 7

Question 1

Define congruent triangles

Answer 1

They have the same shape and size; they have corresponding angles that are equal and corresponding sides that are equal.

Question 2

What symbol means “congruent to”?

Answer 2

= with ~ on top of it

Question 3

If a triangle has three equal sides, are they always congruent?

Answer 3

Yes, they will always be congruent

Question 4

If a triangle has three equal angles, are they always congruent?

Answer 4

Yes, they will always be congruent.

Question 5

What are the three different conditions for congruent triangles?

Answer 5

1. side-side-side congruence (SSS)
2. side-angle-side congruence (SAS)
3. angle-side-angle congruence (ASA)

Question 6

What are the properties of similar triangles?

Answer 6

1. corresponding angles are equal
2. ratios of corresponding sides are equal
3. the ratio of the areas is equal to the square of the ratio of corresponding sides

Question 7

Define similar triangles

Answer 7

They have the same shape but not necessarily the same size.

Question 8

What symbol means “similar to”?

Answer 8

~

Question 9

What are the two conditions of similar triangles?

Answer 9

1. angle-angle similarity (AA~): two pairs of corresponding angles are equal
2. side-side-side similarity (SSS~): the ratios of corresponding sides are equal

Question 10

How do you use similar triangles to measure distances that are difficult to measure (solve word problems)?

Answer 10

1. draw a diagram if one isn’t given to you
2. establish if the two triangles are similar (usually AA~)
3. identify the unknown measurement with a variable
4. set up the ratio and solve for the variable
5. make a final statement, including units