Question 937612: CAT is an isosceles triangle whose vertex angle is
A) it is an obtuse triangle
B) m is less than T = 40
C) AC = AT
D) all of these are true
can you tell me why a or b? and what m means?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! What you meant is
 is an isosceles triangle whose vertex angle is  . The  . What is true about  ?
A) it is an obtuse triangle
B) 
C) AC = AT
D) all of these are true
Can you tell me why A or B? and what  means?
The triangle looks like this:
A symbol looking sort-of like is used to mean "triangle",
so means  .
A symbol looking sort-of like  is used to mean "angle",
so means angle A (angle CAT);
 means angle C (angle ACT), and
 means angle T (angle ATC).
The in front of the symbol means "measure of",
so means the measure of angle C is  .
An isosceles triangle is one that has two "congruent" sides (two sides of equal length).
The other side is called the base.
The angle made by the two congruent sides is called the vertex angle.
The other two angles (the ones adjacent to the base) are called base angles.
The base angles in an isosceles triangle are congruent (they have the same measure).
So, and are the base angles, and both measure , so " " is true.
Since the measures of the angles of any triangle add up to  , the measure of the vertex angle is
 .
Since angle  , the vertex angle, measures  ,
it is an obtuse angle,
and a triangle wit one obtuse angle is called an obtuse triangle,
so " it is an obtuse triangle" is true about .
"  is true because the definition of isosceles triangle is that the two sides that form the "vertex angle" are congruent (have the same measure).
In this case, the two sides that form the vertex angle
(the ones that end at vertex ) are  and  .
So, " all of these are true" is true about .
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