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

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

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.

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 Theorem 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?

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.

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