document.write( "Question 937612: CAT is an isosceles triangle whose vertex angle is \n" ); document.write( "\n" ); document.write( "A) it is an obtuse triangle
\n" ); document.write( "
\n" ); document.write( "B) m is less than T = 40\r
\n" ); document.write( "\n" ); document.write( "C) AC = AT\r
\n" ); document.write( "\n" ); document.write( "D) all of these are true\r
\n" ); document.write( "\n" ); document.write( "can you tell me why a or b? and what m means? \n" ); document.write( "

Algebra.Com's Answer #571057 by KMST(5328) $\"\"$ $\"About$

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What you meant is
\n" ); document.write( " $\"CAT\"$ is an isosceles triangle whose vertex angle is $\"%22%3C+A%22\"$ . The $\"m%3CC=40%5Eo\"$ . What is true about $\"DELTA\"$ $\"CAT\"$ ?
\n" ); document.write( "A) it is an obtuse triangle
\n" ); document.write( "B) $\"m%3CT=40%5Eo\"$
\n" ); document.write( "C) AC = AT
\n" ); document.write( "D) all of these are true
\n" ); document.write( "Can you tell me why A or B? and what $\"m\"$ means?
\n" ); document.write( "
\n" ); document.write( "The triangle looks like this:
\n" ); document.write( "

\n" ); document.write( "
\n" ); document.write( "A symbol looking sort-of like $\"DELTA\"$ is used to mean \"triangle\",
\n" ); document.write( "so $\"DELTA\"$ $\"CAT\"$ means $\"triangle\"$ $\"CAT\"$ .
\n" ); document.write( "A symbol looking sort-of like $\"%22%3C%22\"$ is used to mean \"angle\",
\n" ); document.write( "so $\"%22%3C+A%22\"$ means angle A (angle CAT);
\n" ); document.write( " $\"%22%3C+C%22\"$ means angle C (angle ACT), and
\n" ); document.write( " $\"%22%3C+T%22\"$ means angle T (angle ATC).
\n" ); document.write( "The $\"m\"$ in front of the $\"%22%3C%22\"$ symbol means \"measure of\",
\n" ); document.write( "so $\"m%3CC=40%5Eo\"$ means the measure of angle C is $\"40%5Eo\"$ .
\n" ); document.write( "
\n" ); document.write( "An isosceles triangle is one that has two \"congruent\" sides (two sides of equal length).
\n" ); document.write( "The other side is called the base.
\n" ); document.write( "The angle made by the two congruent sides is called the vertex angle.
\n" ); document.write( "The other two angles (the ones adjacent to the base) are called base angles.
\n" ); document.write( "The base angles in an isosceles triangle are congruent (they have the same measure).
\n" ); document.write( "
\n" ); document.write( "So, $\"%22%3C+C%22\"$ and $\"%22%3C+T%22\"$ are the base angles, and both measure $\"40%5Eo\"$ , so \" $\"highlight%28%22B+%29%22%29\"$ $\"m%3CT=40%5Eo\"$ \" is true.
\n" ); document.write( "
\n" ); document.write( "Since the measures of the angles of any triangle add up to $\"180%5Eo\"$ , the measure of the vertex angle is
\n" ); document.write( "

.
\n" ); document.write( "Since angle $\"A\"$ , the vertex angle, measures $\"100%5Eo%3E90%5Eo\"$ ,
\n" ); document.write( "it is an obtuse angle,
\n" ); document.write( "and a triangle wit one obtuse angle is called an obtuse triangle,
\n" ); document.write( "so \" $\"highlight%28%22A+%29%22%29\"$ it is an obtuse triangle\" is true about $\"DELTA\"$ $\"CAT\"$ .
\n" ); document.write( "
\n" ); document.write( "\" $\"highlight%28%22C+%29%22%29\"$ $\"AC+=+AT\"$ is true because the definition of isosceles triangle is that the two sides that form the \"vertex angle\" are congruent (have the same measure).
\n" ); document.write( "In this case, the two sides that form the vertex angle
\n" ); document.write( "(the ones that end at vertex $\"A\"$ ) are $\"AC\"$ and $\"AT\"$ .
\n" ); document.write( "
\n" ); document.write( "So, \" $\"highlight%28%22D+%29%22%29\"$ all of these are true\" is true about $\"DELTA\"$ $\"CAT\"$ . \n" ); document.write( "

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