Evidence of base angles theorem

The base angles theorem says that if the sides of a triangle are congruent (isosceles triangle) then the angles opposite those sides are congruent

Start with the following isosceles triangle. The two equal parts are presented with a red mark and contrary to these sides angles are also shown in red

base-angles-image

The strategy is to draw the perpendicular bisector of vertex c segment AB

Then use SAS postulate to demonstrate that the trained two triangles are congruent

If the two triangles are congruent, the corresponding angles to be congruent

Draw the perpendicular bisector of c

base-angles-imageSince the angle c is cut in two,

angle (x) = angle (y)

Segment AC = segment BC (it has been given)

FC = FC segment segment (on the side of the commune is the same for the triangle ACF and triangle BCF)

Triangles ACF and triangle BCF are consistent and then by SAS or side angle

In other words, by

AC-angle (x) – FC

and

BC-angle (y) – FC

Since the limit ACF and BCF triangle are congruent, angle angle = B

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