proportions in triangles chapter 7 section 5. objectives students will use the side-splitter theorem...
TRANSCRIPT
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
If three parallelparallel lines intersect two transversals, then the segments intercepted on the transversals are proportional.
AA
BB
CC
DD
EE
FF
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.
AA
BB
CCDD
AD AB
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.