Construct a triangle given a base length of r 
and both base angles of measure α and β.
Use the sliders to choose your length r . 
You can use the added tools
Fill out the chart.

Steps to Make the Construction

α

β

Does this construction always work? Explain why. Use the sliders for the angles to help.

r = 8.7 (slider from 0 to 10, step 0.1)
α = 64.8 (slider from 0 to 360, step 0.1)
β = 37.8 (slider from 0 to 360, step 0.1)
a_1: abs(r)
D = (-2.02, 0.34)
E = (-3.84, 0.38)
D' = Rotate(D, α°, E)
ε = Angle(D, E, D')
F = (-1.8, -1.74)
G = (-3.9, -1.76)
F' = Rotate(F, β°, G)
ζ = Angle(F, G, F')
d = Segment(F, G)
e = Segment(G, F')
f = Segment(D, E)
g = Segment(E, D')

Tool: Angle with given size - counterclockwise (command Anglewithgivensize)
Input: B, A, α
Output: γ, c

B' = Rotate(B, α°, A)
c = Ray(A, B')
γ = Angle(B, A, B')

Tool: Angle with a given side - clockwise (command Anglewithagivenside)
Input: A, B, β
Output: δ, c

A' = Rotate(A, (-(β°)), B)
δ = Angle(A', B, A)
c = Ray(B, A')