1. 7.2(a) Notes: Medians of Triangles
Date:
7.2(a) Notes: Medians of Triangles
Lesson Objective: Identify and use medians in triangles
CCSS: G.CO.10, G.MG.3
You will need: colored pens, CR
Real-World App: What are the coordinates so that a triangle can balance?
This is Jeopardy!!!:  This is what the segment bisector does to a segment.

2. Lesson 1: The Centroid Theorem
Label the vertices of your triangle A, B and C. B
A C

3. Lesson 1: The Centroid Theorem
Bisect AB by pin­ching it at the halfway point. La­bel the bisector X. B X
A C

4. Lesson 1: The Centroid Theorem
Draw a line from X to C.
Mark the congruent segments. B X
A C

5. Lesson 1: The Centroid Theorem
Bisect BC and label the bi­sector Y. Draw AY. Bisect AC and label the bisector Z. Draw BZ. B
X Y
A Z C

6. • Lesson 1: The Centroid Theorem
Mark all congruent segments. Label the point of intersection P. B
P (Centroid)
X Y
A Z C •

7. • Lesson 1: The Centroid Theorem
Try bal­an­cing the triangle on your pencil with the point of your pencil at P. What do you notice? B
P (Centroid)
X Y
A Z C •

8. • Lesson 1: The Centroid Theorem Median: Midpoint to Vertex
AY, BZ and CX are medians B
P (Centroid)
X Y
A Z C
Centroid Theorem: The centroid of a ∆ is located 2/3 of the distance from each vertex to the midpoint of the opposite side. It is the point of balance. •

9. • Lesson 1: The Centroid Theorem AP = 2/3AY BP = 2/3BZ CP = 2/3CX
Because 2/3 + 1/3 = 1, then
YP = 1/3AY ZP = 1/3BZ XP = 1/3CX
Median: Midpoint to Vertex
AY, BZ and CX are medians B
P (Centroid)
X Y
A Z C •

10. • Lesson 2: Using the Centroid to Find Segment Lengths
In ∆ABC, P is the centroid, AY = 9, and PX = Find each length.
A. AP B. CX B
P (Centroid)
X Y
A Z C •

11. Lesson 3: Finding the Centroid on the Coordinate Plane

12. Lesson 3: Finding the Centroid on the Coordinate Plane
A(1, 10), B(5, 0), C(9, 5)

13. 7.2(a): Do I Get It?
In ΔABC, Q is the centroid
and BE = 27. Find BQ and QE.
Find AD if AQ = 15.
A second triangle like the
one in Lesson 3 has vertices at
X(-3, 0), Y(0, -8) and Z(-6,-4).
Find the coordinates of the
point where the artist should
support the triangle so that it
will balance. Explain your
reasoning.