7. Construct a Triangle Given the Lengths of Two Sides and a Median of the Third Side
7. Construct a Triangle Given the Lengths of Two Sides and a Median of the Third Side
This Demonstration shows a construction of a triangle given the lengths of two sides and and the length of the median from to .
ABC
BC=a
CA=b
m
C
AB
Construction
Let be a line segment of length and midpoint .
EC
2m
D
Step 1: Draw a circle with center and radius and a circle with center and radius . Let and be the intersections of the circles.
E
b
C
a
B
B'
Step 2: Extend past to such that . The triangle has side of length , since is a parallelogram with sides and . Similarly, . Finally, is a median of length .
BD
D
A
BD=DA
ABC
CA
b
EACB
a
b
BC=a
DC
m