SOLUTION: 4.Cake.Carl has a piece of cake in the shape of an isosceles triangle with angles 26 � ,77 � , and 77 �. He wanted to divide it into two equal parts, so he cut it through the middl

Question 698434: 4.Cake.Carl has a piece of cake in the shape of an isosceles triangle with angles 26 � ,77 � , and 77 �. He wanted to divide it into two equal parts, so he cut it through the middle of the 26 � angle to the midpoint of the opposite side. He says that because he is dividing it at the midpoint of a side, the two pieces are congruent. Is this enough information? Explain. please explain step by step.
Answer by sofiyac(983) (Show Source): You can put this solution on YOUR website!
Carl is correct, he has cut the large piece into 2 equal smaller pieces.

However, his explanation is not complete.

What he drew was not only an angle bisector, but more importantly, a median!

When you draw a median of a triangle, it does indeed cut the other side into 2 equal segments.

Now, Carl has 2 small triangles.

But are they congruent? That is the question.

Let's label our large triangle ABC, with A being the vertex with the 26 degree angle.

Let's call the midpoint of the segment opposite vertex A, point D.

Now, the 2 triangles that are formed are triangle ADB, and triangle ADC.

Can we tell if these are congruent? We can, here's how:

AB is congruent to AC since it is an isoscoles triangle.

BD is congruent to CD since D is the midpoint of BC.

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