Question 1081439


Start with the following isosceles triangle. The two equal sides are shown with one red mark and the angles opposites to these sides are also shown in red.


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The strategy is to draw the perpendicular bisector from vertex {{{C}}} to segment {{{AB}}}.

Then use {{{SAS}}} postulate to show that the two triangles formed are congruent.

If the two triangles are congruent, then corresponding angles to will be congruent.

Draw the perpendicular bisector from {{{C}}}.


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Since angle {{{C}}} is bisected,we got

angle {{{x}}} and angle {{{y}}} which are same measure; so,  angle {{{ x= y}}}

Segment {{{AC =  BC}}}... ( This one was {{{given}}})

Segment {{{CF = CF }}}(Common side is the same for both triangle {{{ACF}}} and triangle {{{BCF}}})

Triangles {{{ACF}}} and triangle {{{BCF}}} are then congruent by {{{SAS}}} or {{{side-angle-side}}}.

In other words, by

{{{AC}}}-angle({{{x}}})-{{{CF}}}

and

{{{BC}}}-angle({{{y}}})-{{{CF}}}

Since triangle {{{ACF}}} and triangle {{{BCF}}} are congruent, angle {{{A}}} = angle{{{ B}}}