Proportional Segments in Triangles

The Side-Angle-Side Similarity (SAS ~) Theorem states that if two sides of one triangle are ________________ to two sides of another triangle and their _________________ angles are congruent, then the triangles are similar.

• adjacent; intersect

• complementary; form

• adjacent; create

• proportional; included

Find the missing length.

• 6

• 8

• 5

• None of these

What is the Triangle-Angle-Bisector Theorem

• If a ray bisects a segment of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle.

• If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle.

• If a ray bisects an angle of a triangle, then it divides the opposite side into three segments that are proportional to the other two sides of the triangle.

• If a ray bisects an segment of a triangle, then it divides the opposite side into three segments that are proportional to the other two sides of the triangle.

Find the missing length.

• 10

• 21

• 35

• 9

Find the missing length.

• 15

• 11

• 35

• 8

Find the missing length.

• 21

• 18

• 16

• 24

What is the side splitter theorem?

• If a line is perpendicular to one side of a triangle and intersects the other three sides, then it divides those side proportionally.

• If a line is parallel to one side of a triangle and intersects the other three sides, then it divides those side proportionally.

• If a line is perpendicular to one side of a triangle and intersects the other two sides, then it divides those side proportionally.

• If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those side proportionally.

What is X

• 9

• 7

• 4

• 6

Find the missing length.

• 25

• 15

• 6

• 16

Given the figure on top, which two triangles are similar?

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