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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