- Find the length of each side of the triangle with the following vertices with the distance formula. Then classify
each triangle by its sides.
a)( 3 , 1 ),( 3 , 5 ), and( 10 , 3 )
Answer: The triangle is isosceles with side lengths: 4,
√
51, and√
51.
b)(− 3 , 2 ),(− 8 , 3 ), and(− 3 ,− 5 )
Answer: This triangle is scalene with side lengths: 7,
√
26, and√
89.
Sometimes students have trouble seeing that they need to take the points two at a time to find the side lengths. By
graphing the triangle on graph paper before using the distance formula they can see how to find the side lengths. If
they graph the triangle they can also classify it by its angles.
Problem Solving in Geometry
Don’t Panic –Problem solving and applications are particularly challenging for many students. Sometimes they
just give up. Let the students know that this is difficult. They are probably going to struggle, have to reread the
information several time, and will be confused for a while. It is all part of the process. This section will give them
strategies to work through the difficulties.
Highlight Important Information –It is nice when students can actually mark up the text of the exercise, but
frequently this is not the case. As they read the paragraph have the students take notes or organize the information
into a chart. Otherwise the students can just get lost in all the words. Translating from English to math is often the
hardest part.
The Last Sentence –When the students are faced with a sizable paragraph of information the most important
sentence, the one that asks the question, is usually at the end. Advise the students to read the last sentence first, then
as they read the rest of the paragraph they will see how the information they are being given is important.
Does This Make Sense? – It is so hard to get the students to ask themselves this question at the end of a word
problem or application. I think they are so happy to have an answer they do not want to know if it is wrong. Keep
reminding them. Sometimes it is possible to not accept work with an obviously wrong answer. The paper can be
returned to the student so they can look for their mistake. This is a good argument for the importance of showing
clear, organized work.
Naming Quadrilaterals– When naming a quadrilateral the letter representing the vertices will be listed in a
clockwise or counterclockwise rotation starting from any vertex. Students are accustomed to reading from left
to right and will sometimes continue this pattern when naming a quadrilateral.
The Pythagorean Theorem– Most students have learned to use the Pythagorean Theorem before Geometry class
and will want to use it instead of the distance formula. They are closely related; the distance formula is derived from
the Pythagorean Theorem as will be explained in another chapter. If they are allowed to use the Pythagorean Theorem
remind them that it can only be used for right triangles, and that the length of the longest side of the right triangle,
the hypotenuse, must be substituted into the[U+0080][U+009C]c[U+0080][U+009D]variable if it is know. If the
hypotenuse is the side of the triangle being found, the[U+0080][U+009C]c[U+0080][U+009D]stays a variable, and
the other two side are substituted for[U+0080][U+009C]a[U+0080][U+009D]and[U+0080][U+009C]b[U+0080][U+009D].
2.1. Basics of Geometry