# 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