Question 202822
Prove: If the base angles of a triangle are congruent, then the triangle is isosceles. 

Given: Triangle BAC with angle B = angle C 
To Prove: Triangle is isosceles. 
Construction:
Draw a perpendicular line from vertex A on side BC which meets side BC at L. 
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Draw triangle ABC with B = C
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Draw a perpendicular from A to side BC forming Angle ALB and Angle ALC
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Prove ABC is isosceles.
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Proof:
B = C---------------------------Given
Angle ALB1 = Angle ALC = 90-----def of perpendicular line
AL = AL-------------------------identity
tri LBA congruent to tri LCA----angle-side-angle theorem
BA = CA-------------------------corresponding parts of congruent triangles
tri ABC is isosceles------------definition of isosceles triangle
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Cheers,
Stan H.