Similar Triangles Proportions Angle Bisector

Determine whether the triangles are similar or not. If so, state how they are similar.

• Yes, by AA Similarity

• Yes, by SAS Similarity

• Yes, by SSS Similarity

• No, not similar

Find the missing side using proportions.

• a

• b

• c

• d

Find the missing side using proportions.

• a

• b

• c

• d

When proving these triangles similar, what would you write in for the missing reason?

• Math

• Corresponding sides are proportional

• Corresponding sides are congruent

• SSS similarity postulate

• ABC
• BDE
• CD
• AE

Complete each proportion.
AB / BM  =  ? / CD

• BC

• AC

• MD

• MC

What is the Angle Bisector Theorem?

• The Angle Bisector Theorem states that in a triangle, the angle bisector of a side divides the opposite side into segments that are proportional to the lengths of the other two sides.

• The Angle Bisector Theorem states that in a triangle, the angle bisector of a side divides the opposite side into segments that are perpendicular to the adjacent sides.

• The Angle Bisector Theorem states that in a triangle, the angle bisector of a side divides the opposite side into segments that are proportional to the lengths of the adjacent sides.

Determine the Conclusion.

• Then ∠BCA ≅ ∠DCA.

• Then ∠BAC ≅ ∠DAC.

• Then Segment AB is congruent to Segment AD.

• Then ∠BAC and ∠DAC are right angles.

If QS is an angle bisector, solve for x.

• 9

• 2.8

• 10

• 8.2

If $\overline{QS}$ represents an angle bisector, solve for x.