7. Construct a Triangle Given the Lengths of Two Sides and a Median of the Third Side

a

b

m

step 1

step 2

This Demonstration shows a construction of a triangle

ABC

given the lengths of two sides

BC=a

and

CA=b

and the length

m

of the median from

C

to

AB

.

Construction

Let

EC

be a line segment of length

2m

and midpoint

D

.

Step 1: Draw a circle with center

E

and radius

b

and a circle with center

C

and radius

a

. Let

B

and

B'

be the intersections of the circles.

Step 2: Extend

BD

past

D

to

A

such that

BD=DA

. The triangle

ABC

has side

CA

of length

b

, since

EACB

is a parallelogram with sides

a

and

b

. Similarly,

BC=a

. Finally,

DC

is a median of length

m

.