# 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