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