Segment Sleuth Worksheet
Geometry Lab • Special Triangle Segments CCSS.MATH.HSG.CO.C.10
Segment Sleuth Challenge
Examine the geometric markings to identify medians, altitudes, and bisectors.
Name
Date
Period
Diagram: Scalene Triangle \(\triangle ABC\) Pay close attention to angle arcs, tick marks, right-angle boxes, and vertices.
A B C H D M A B C D
Key Endpoints: \(H\) is on \(BC\), \(D\) is on \(BC\), \(M\) is on \(BC\). Note: Triangle \(ABC\) is scalene (\(AB \neq AC \neq BC\)).
1 Primary Challenge: Which segment is the MEDIAN?
Target Question
Segment A
Segment B
Segment C
Segment D
Mathematical Justification: Explain how you know your choice is the median. Cite the geometric definition and specific markings:
2 Classification: Identify & Verify All Four Segments
| Segment | Special Segment Type | Visual Evidence / Markings from Diagram |
|---|
| Segment A | | |
| Segment B | | |
| Segment C | | |
| Segment D | | |
3 Critical Analysis: Median vs. Perpendicular Bisector
Both Segment C and Segment D intersect side \(BC\) at point \(M\). Why is Segment C a median while Segment D is a perpendicular bisector? Under what special condition for \(\triangle ABC\) would these two lines coincide?
