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WARM UP: What similarity statement can you write relating the three triangles in the diagram? What is the geometric mean of 6 and 16? What are the values.

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Presentation on theme: "WARM UP: What similarity statement can you write relating the three triangles in the diagram? What is the geometric mean of 6 and 16? What are the values."— Presentation transcript:

1 WARM UP: What similarity statement can you write relating the three triangles in the diagram? What is the geometric mean of 6 and 16? What are the values of x, y, and z? z

2 7.5 - Proportions in Triangles
I can use the Side-Splitter Theorem and the Triangle-Bisector Theorem.

3 Side – Splitter Theorem
When two or more parallel lines intersect other lines, proportional segments are formed. Side – Splitter Theorem Theorem If… Then… If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.

4 Problem: Using the Side-Splitter Theorem
What is the value of x in the diagram at the right?

5 Problem: Using the Side-Splitter Theorem
What is the value of “a” in the diagram at the right?

6 Problem: Using the Side-Splitter Theorem
What is the value of x in the diagram?

7 Corollary to the Side-Splitter Theorem
If… Then… If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional.

8 Problem: Finding a Length
Three campsites are shown in the diagram. What is the length of Site A along the river?

9 Problem: Finding a Length
What is the length of Site C along the road?

10 Problem: Finding a Length
Two plots of land are shown below. What is the unknown length, x?

11 Triangle – Angle Bisector Theorem
The bisector of an angle of a triangle divides the opposite side into two segments with lengths proportional to the sides of the triangle that form the angle. Triangle – Angle Bisector Theorem Theorem If… Then… 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.

12 Problem: Using the Triangle-Angle- Bisector Theorem
What is the value of x in the diagram?

13 Problem: Using the Triangle-Angle- Bisector Theorem
What is the value of y in the diagram?

14 Problem: Using the Triangle-Angle- Bisector Theorem
What is the value of x in the diagram?

15 After: Lesson Check

16 Homework: Page 475, #10 – 22 even, 25,26,31,33

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