WARM UP:1. What similarity statement can you write

relating the three triangles in the diagram?

2. What is the geometric mean of 6 and 16?

3. What are the values of x, y, and z?

z

7.5 - Proportions in TrianglesI can use the Side-Splitter Theorem and the Triangle-Bisector Theorem.

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

Side – Splitter TheoremTheorem 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.

Problem: Using the Side-Splitter Theorem

•What is the value of x in the diagram at the right?

Problem: Using the Side-Splitter Theorem

•What is the value of “a” in the diagram at the right?

Problem: Using the Side-Splitter Theorem

•What is the value of x in the diagram?

Corollary to the Side-Splitter TheoremCorollary If… Then…

If three parallel lines intersect

two transversals,

then the segments

intercepted on the transversals

are proportional.

Problem: Finding a Length

•Three campsites are shown in the diagram. What is the length of Site A along the river?

Problem: Finding a Length

•What is the length of Site C along the road?

Problem: Finding a Length

•Two plots of land are shown below. What is the unknown length, x?

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 TheoremTheorem 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.

Problem: Using the Triangle-Angle- Bisector Theorem

•What is the value of x in the diagram?

Problem: Using the Triangle-Angle- Bisector Theorem

•What is the value of y in the diagram?

Problem: Using the Triangle-Angle- Bisector Theorem

•What is the value of x in the diagram?

After: Lesson Check

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