8.2: SideSplitter Theorem
This activity is intended to supplement Geometry, Chapter 7, Lesson 5.
ID: 12318
Time Required: 15 minutes
Activity Overview
In this activity, students will explore the sidesplitter theorem.
Topic: Ratio, Proportion & Similarity
 SideSplitter Theorem
Teacher Preparation and Notes
 This activity was written to be explored with the Cabri Jr. app on the TI84.
 To download Cabri Jr, go to http://www.education.ti.com/calculators/downloads/US/Software/Detail?id=258#.
 To download the calculator files, go to http://www.education.ti.com/calculators/downloads/US/Activities/Detail?id=12318 and select SIDESP1, SIDESP2, and SIDESP3.
Associated Materials
 Student Worksheet: SideSplitter Theorem http://www.ck12.org/flexr/chapter/9692, scroll down to the second activity.
 Cabri Jr. Application
 SIDESP1.8xv, SIDESP2.8xv, and SIDESP3.8xv
Problem 1 – SideSplitter Theorem
Students will begin this activity by looking at the sidesplitter theorem. Students are given a triangle with a segment parallel to one side. They will discover that if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.
Students will be asked to collect data by moving point
Problem 2 – Application of the SideSplitter Theorem
In Problem 2, students will be asked to apply the sidesplitter theorem to several homework problems.
Problem 3 – Extension of the SideSplitter Theorem
In Problem 3, students will discover the corollary to the SideSplitter Theorem: If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.
Students are asked several questions about the corollary to the sidesplitter theorem.
Solutions
1. Sample answers:
Position 







1  4.1  1.8  4.6  2.0  2.27  2.30 
2  3  2.8  3.4  3.2  1.07  1.06 
3  2.6  2.4  3.2  3.0  1.08  1.07 
4  3.3  3.1  2.5  2.3  1.06  1.08 
2. The ratios of the side lengths are equal.
3.
4. The ratio remains the same.
5. The ratio changes when moving point
6. When you move the parallel line, you are changing the proportion between the upper and lower segments. When you move the point, the segments may get longer or shorter, but the proportion stays the same.
7.
8.
9. Sample answers:
Position 







1  2.1  1.5  2.4  1.8  1.4  1.4 
2  2.1  1.3  2.7  1.7  1.6  1.6 
3  1.9  1.5  2.4  2.0  1.2  1.2 
4  2.7  0.7  3.5  0.9  4  4 
10. The ratios are equal.
11.
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