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# 8.2: Side-Splitter Theorem

Created by: CK-12

This activity is intended to supplement Geometry, Chapter 7, Lesson 5.

## Problem 1 – Side Splitter Theorem

In SIDESP1.8xv, you are given $\triangle{CAR}$. You are also given $\overline{DS}$ which is parallel to side $CR$.

1. Move point $D$ to 2 different positions and point $A$ to 2 different positions and collect the data in the table below. Calculate the ratios of $AD$ to $DC$ and $AS$ to $SR$ for each position and record the calculation in the table below.

Position $AD$ $DC$ $AS$ $SR$ $\frac{AD}{DC}$ $\frac{AS}{SR}$
1
2
3
4

2. Make some observations about the ratios of the sides in the triangle. What relationships do you notice?

3. Use the table to complete the following conjecture about the relationship between $\frac{AD}{DC}$ and $\frac{AS}{SR}$. If side $DS$ is parallel to side $CR$, then _____________.

4. In SIDESP2.8xv, drag point $A$. Make some observations about the relationship of the ratios $\frac{AD}{DC}$ and $\frac{AS}{SR}$?

5. In SIDESP2.8xv, drag point $D$. Make some observations about the relationship of the ratios $\frac{AD}{DC}$ and $\frac{AS}{SR}$?

6. Why are the results different when moving point $A$ versus moving point $D$?

## Problem 2 – Application of the Side-Splitter Theorem

7. Find the value of $x$.

8. Find the value of $x$.

## Problem 3 – Extension of the Side-Splitter Theorem

For this problem, we will look at a corollary of the side-splitter theorem.

9. In SIDESP3.8xv, move point $U$ to 2 different positions and point $N$ to 2 different positions and collect the data in the table on the accompanying worksheet.

Position $RN$ $NO$ $EA$ $AS$ $\frac{RN}{NO}$ $\frac{EA}{AS}$
1
2
3
4

10. What do you notice about the ratios $\frac{RN}{NO}$ and $\frac{EA}{AS}$?

11. Use the table to complete the following conjecture about the relationship between $\frac{RN}{NO}$ and $\frac{EA}{AS}$. If lines $RE$, $NA$, and $OS$ are parallel and cut by two transversals, then ________________________.

Feb 23, 2012

Nov 03, 2014