Entry Task Find the value of x in each figure x 4 x 6 14
Proportions in Triangles Lesson 7-5
Investigation 1 Parallels and Proportionality For this investigation you will need a ruler and a protractor. Step 1: In the figure below, find the value of x x A D B E C 8 12 D E C 8 16 x A D B 24 x + 12 A D B
Now let’s see if the converse is true? Complete steps 3-9 of Investigation 1. When you are finished, use your observations to write a conjecture about the ratios of the lengths of the segments that are cut off by parallel lines. Our book calls this theorem the Side-Splitter Theorem. If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally. The converse of this theorem is also true: If a line divides two sides of a triangle proportionally, then it is parallel to the third side.
Corollary to the Side-Splitter Theorem This extends the theorem to multiple parallel lines. If three parallel lines intersect on two transversals, then the segments intercepted on the transversal are proportional.
Investigation 2 Complete this investigation and compare your results with others near you. Use your observations to write a conjecture.
Triangle-Angle-Bisector Theorem The angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle.
Lesson Check Find the value of x in each figure Find the value of x and y in the figure.
One more investigation… Investigating corresponding parts of triangles. In this investigation, you will look at the relationship between corresponding altitudes, corresponding medians, and corresponding angle bisectors of similar triangles. Proportional Parts Conjecture: If two triangles are similar, then the corresponding altitudes, medians, and angle bisectors are proportional to the corresponding sides.
Homework Page 475 (10-22 evens, all, evens)