Proportions in Triangles Chapter 7 Section 5. Objectives Students will use the Side-Splitter Theorem...

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Proportions in Triangles Chapter 7 Section 5

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Transcript of Proportions in Triangles Chapter 7 Section 5. Objectives Students will use the Side-Splitter Theorem...

Page 1: Proportions in Triangles Chapter 7 Section 5. Objectives Students will use the Side-Splitter Theorem and the Triangle-Angle- Bisector Theorem.

Proportions in Triangles

Chapter 7 Section 5

Page 2: Proportions in Triangles Chapter 7 Section 5. Objectives Students will use the Side-Splitter Theorem and the Triangle-Angle- Bisector Theorem.

Objectives

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

Page 3: 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?

Page 4: Proportions in Triangles Chapter 7 Section 5. Objectives Students will use the Side-Splitter Theorem and the Triangle-Angle- Bisector Theorem.

Remember

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

Page 5: Proportions in Triangles Chapter 7 Section 5. Objectives Students will use the Side-Splitter Theorem and the Triangle-Angle- Bisector Theorem.

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).

Page 6: Proportions in Triangles Chapter 7 Section 5. Objectives Students will use the Side-Splitter Theorem and the Triangle-Angle- Bisector Theorem.

Turn to page 472…

Look at Problem 1

Try the “Got It” problem for that example.

Page 7: Proportions in Triangles Chapter 7 Section 5. Objectives Students will use the Side-Splitter Theorem and the Triangle-Angle- Bisector Theorem.

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?

Page 8: Proportions in Triangles Chapter 7 Section 5. Objectives Students will use the Side-Splitter Theorem and the Triangle-Angle- Bisector 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

Page 9: Proportions in Triangles Chapter 7 Section 5. Objectives Students will use the Side-Splitter Theorem and the Triangle-Angle- Bisector Theorem.

On Page 473…

Look at Problem 2

Try the “Got It” for this example

Page 10: Proportions in Triangles Chapter 7 Section 5. Objectives Students will use the Side-Splitter Theorem and the Triangle-Angle- Bisector Theorem.

Question:

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

Page 11: Proportions in Triangles Chapter 7 Section 5. Objectives Students will use the Side-Splitter Theorem and the Triangle-Angle- Bisector Theorem.

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

Page 12: Proportions in Triangles Chapter 7 Section 5. Objectives Students will use the Side-Splitter Theorem and the Triangle-Angle- Bisector Theorem.

On page 474

Look at Problem 3

Page 13: Proportions in Triangles Chapter 7 Section 5. Objectives Students will use the Side-Splitter Theorem and the Triangle-Angle- Bisector Theorem.

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?

Page 14: Proportions in Triangles Chapter 7 Section 5. Objectives Students will use the Side-Splitter Theorem and the Triangle-Angle- Bisector Theorem.

On page 474…

Try problems #1-8 on your own.

Page 15: Proportions in Triangles Chapter 7 Section 5. Objectives Students will use the Side-Splitter Theorem and the Triangle-Angle- Bisector Theorem.

Exit Slip/Reflection

1. What is the Side-Splitter-Theorem?

2. What is the Triangle-Angle-Bisector Theorem?

3. Give an example of each.


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