Geometry
Ch. 5: Relationships w/in Triangles
Investigate: Segments in Triangles
Name: ___________________________________________________
Date: ____________________________________________________
Objective- To determine how the midsegment of a triangles is related to the sides of a triangle.
Vocabulary- A midsegment is a segment of a triangle that connects the midpoints of two sides of a
triangle.
Step 1: Draw a right triangle with legs on the x-axis and yaxis.
Use vertices A (0, 8); B (6, 0); O (0, 0) as Case 1.
̅̅̅̅ and 𝑂𝐵
̅̅̅̅. Plot the
Step 2: Find the midpoints of 𝑂𝐴
midpoints and label them D and E. Connect them to create
segment ̅̅̅̅
𝐷𝐸 .
Step 3: Draw a Case 2 triangle. Copy and complete the
table below.
Draw Conclusions:
1. Choose two other right triangles with legs on the axes. Add these triangles as Cases 3 and 4 to your table.
2. Add to your table and complete Case 5 if A(0, n); B ( k, 0) and O (0, 0).
3. Add to your table and complete Case 6 if A(0, 2n); B (2k, 0) and O (0, 0).
4. What do you notice about the slopes of ̅̅̅̅
𝐴𝐵 and ̅̅̅̅
𝐷𝐸 ? What do you notice about the lengths of ̅̅̅̅
𝐴𝐵 and ̅̅̅̅
𝐷𝐸 ?
̅̅̅̅? Explain.
5. In each case, is the midsegment ̅̅̅̅
𝐷𝐸 parallel to 𝐴𝐵
6. Are your observations true for the midsegment created by connecting the midpoints of ̅̅̅̅
𝑂𝐴 and ̅̅̅̅
𝐴𝐵 ? What
̅̅̅̅
̅̅̅̅
about the midsegment connecting midpoints of 𝐴𝐵 and 𝑂𝐵?
7. Make a conjecture (in if-then form) about the relationship between a midsegment and the third side of a
triangle.
Try It Out!
1.
2.