One day triangle SAM

met 

 TOM. They

were different colors but the same shape.  TOM had been told he was an Isosceles Triangle.  SAM had never been told or ever heard of an Isosceles Triangle.  TOM can you define what an Isosceles Triangle is?  Maybe I am one too. 

Well SAM and Isosceles Triangle has two congruent LEGS (sides) that are opposite of each other. I also have two opposite base angles that are congruent. 

"How many types of triangles are there?" asked SAM.   TOM said six three based on their sides like me and three base on angles. 

sides= scalene, isosceles, equilateral

angles= right, acute, obtuse

       base 33 length

TOM explained more characteristics of an Isosceles Triangle has a base that is not congruent with the sides. It also has a vertex angle that is formed by the two legs only.

vertex angle>

See my legs are the same in length but my base is much longer than my legs.

    20              20

65

50

65

TOM also went on to explain if two angles of a triangle are congruent, then the sides opposite those angles are congruent.  You can see my base angles are the same which makes me an Isosceles triangle. But there is a few more things.

TOM then stated "if two sides of a triangle are congruent, then the angles opposite those sides are congruent." Just like mine see. 

24 

24

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Then TOM told SAM "if a line bisects the vertex angle of an Isosceles Triangle, then the line is also the perpendicular bisector of the base".  Just like mine.

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 perpendicular bisector 

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SAM what do you know about your sides and angles"? Asked TOM

" Well, TOM all of my side are the same length. I think it is called equilateral". said SAM 

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"That is very different than my side. What do you know about your angles?" asked TOM .

 "All of my angles are also the same in measure. I think it is called equiangular." said SAM.

equilateral and equiangular???