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WOLFRAM|DEMONSTRATIONS PROJECT

9. Construct a Triangle Given the Length of Its Base, the Difference of the Base Angles and the Sum of the Other Two Sides

step 1

step 2

verification

This Demonstration shows a construction of a triangle

ABC

given the length of the base

AB=c

, the sum

of the other two sides

and

, and the difference

of the base angles.

Construction

Draw a line segment

of length

Step 1: Draw a circle with center

so that the central angle

∠DSB=π-δ

. Measure out the point

at distance

from

Step 2: Let the point

be the intersection of the perpendicular bisector of

and

Verification

Let

∠CAB=α

∠ABC=β

and

∠BCA=γ

Since

∠DSB=π-δ

by construction,

∠DAB=π/2+δ/2

. On the other hand,

∠DAB=α+γ/2=α+(π-α-β)/2=π/2+(α-β)/2

, so

δ=α-β

. Since

DAC

is isosceles,

AC+CB=DB

. By construction,

AB=c

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