Chapter 10: Similar Triangles

Question 1

Definition 51: The ratio of two numbers a and b (b not equal to 0) is

Answer 1

the quotient of the numbers; it’s written as a/b or a : b

Question 2

Definition 52: A proportion is an equation which states that

Answer 2

two ratios are equal to each other; it’s written as a/b=c/d or as a : b = c : d (b and d are not equal to 0)

Question 3

Definition 53: In the proportion a/b=c/d, b and c are referred to as…. and a and d are referred to as…

Answer 3

(b and c) the means of the proportion, and the (a and d) extremes of the proportion

Question 4

Definition 54: If a/b=b/c, then b is

Answer 4

the geometric mean of a and c (where a, b, and c are positive)

Question 5

Theorem 50: In a proportion, the product of the means is

Answer 5

equal to the product of the extremes

Question 6

Definition 55: Definition of Similar Figures: If the vertices of two polygons can be paired so that corresponding angles are congruent and the lengths of corresponding sides are in proportion, then

Answer 6

the polygons are similar

Question 7

Postulate 14: If a line is parallel to one side of a triangle and intersects the other two sides, then

Answer 7

the line divides those sides proportionally

Question 8

Postulate 15: If a line intersects two sides of a triangle and divides those sides proportionally, then

Answer 8

the line is parallel to the third side

Question 9

Theorem 51: Angle-Angle Similarity Theorem (A.A. Similarity): If two angles of one triangle are congruent to two angles of another triangle, then

Answer 9

the triangles are similar

Question 10

Theorem 52: Side-Angle-Side Similarity Theorem (S.A.S. Similarity): If a pair of corresponding angles of two triangles is congruent and the sides including those angles are proportional, then

Answer 10

the triangles are similar

Question 11

Postulate 16: Side-Side-Side Similarity Postulate (S.S.S. Similarity): If all three pairs of corresponding sides of both triangles are proportional, then

Answer 11

the triangles are similar

Question 12

Corollary 51.1: Two triangles similar to a third triangle are

Answer 12

similar to each other

Question 13

Definition 56: Converse of the Definition of Similar Triangles: If two triangles are similar, then their vertices can be paired in correspondence so that all pairs of corresponding angles are __________ and all pairs of corresponding sides are ________.

Answer 13

congruent; proportional

Question 14

Theorem 53: If two triangles are similar, then the lengths of a pair

Answer 14

?