Proportions in Triangles Chapter 7 Section 5

Objectives Students will use the Side-Splitter Theorem and the Triangle-Angle- Bisector Theorem

Question? How do you know if two triangles are similar?

Remember When two or more parallel lines intersect other lines, proportional segments are formed.

Side Splitter Theorem (7-4) If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally (creates two proportional triangles).

Turn to page 472… Look at Problem 1 Try the “Got It” problem for that example.

Question What condition of the Side-Splitter Theorem is marked in the diagram for Problem 1? In other words, what is marked in the figure that lets us know we can use the Side-Splitter Theorem?

Corollary to the Slide-Splitter Theorem parallel If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional. A B C D E F

On Page 473… Look at Problem 2 Try the “Got It” for this example

Question: Should the numerators and the denominators of each ratio in the proportion be corresponding sides of the figure?

Triangle-Angle-Bisector Theorem (7-5) 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. A B C D ADAB DC=CB

On page 474 Look at Problem 3

Question Using the diagram for Problem 3, and considering the properties of proportions, how can the proportion be rewritten so that the x is in a numerator?

On page 474… Try problems #1-8 on your own.

Exit Slip/Reflection 1.What is the Side-Splitter-Theorem? 2.What is the Triangle-Angle-Bisector Theorem? 3.Give an example of each.