Download Classifying

Triangles
“We see triangles in our life on a daily basis such as
the video that I am going to show you. This will
play for the next minute and a half. It will show you
what is done with the triangle instrument,
especially in music. Please keep in mind what type
of triangle you will see and write your guess in your
notes.
http://youtu.be/3rf2fU0bt0I
Angles and Triangles
“As you’ve accessed the website,
www.regentsprep.org and going to the ‘Geometry’
section, specifically the ‘Angles and Triangles’
portion, you can see that triangles are classified by
sides. From the pictures that you see, these
triangles are categorized into three parts: Scalene,
isosceles, and equilateral.”
http://www.regentsprep.org/Regents/math/geome
try/GP5
Sides of Triangles
0 Accessing the www.regentsprep.org to go to the
Geometry section, the sides of triangles.
0 Each triangle is classified by scalene, isosceles and
equilateral. Can you think of what type of triangle
that was used in the YouTube video about the
triangle instrument? The triangle that was used
was an equilateral triangle.
Scalene Triangles
When you look at the scalene triangle. All the sides
are different lengths or do not have congruent sides.
How many remember what the word, congruence,
means? Discuss within your group for a minute,
please and then I’ll choose a group for an answer.
(Ans: equal) Remember that term for the next slide.
Isosceles triangle
Within the website, www.regentsprep.org, that we
are continuing about our discussion about
triangles. The next type of triangle is an isosceles
which displays two congruent sides. Note the
congruent symbols of the sides. Also, look at the
triangle which is labeled as two legs and a base.”
Please continue and click to view the isosceles
triangle.
http://www.regentsprep.org/Regents/math/geometry
/GP5/
Equilateral triangle
0 From the website, www.regentsprep.org, we are
looking at the sides of triangles.
0 Think about the next one: equilateral which also
means ‘equal sides.’ This has three sides and
again, look at the image which shows each side
being equal to 10.
0
http://www.regentsprep.org/Regents/math/geo
metry/GP5/LTriangle.htm
Angles of triangles
0 At the website, www.regentsprep.org, discussing
the angles of a triangle.
0 Here you have four types but this time, it is the
ANGLES, not the sides. They are acute, right,
obtuse, and equiangular triangles. Please note
that all the insides add up to? Please discuss
within your groups and I will call upon that group.
(The answer is 180 degrees)
0 www.regentsprep.org/Regents/math/geometry/a
ngles
Acute triangle
0 In viewing the website, regentsprep.org about
triangles and its angles. Our focus is on:
0 Acute triangles are just that---cute. See how small
their angles are? The triangle show all angles less
than 90 and when added, it should be 180
degrees.
0 Acute triangle
Right triangle
0 At the website, regentsprep.org about triangles.
0 The right triangle has a small box or 90 degrees
that shows you that it has a right angle. If you
remember the Pythagorean Theorem for right
triangles, the longest side is called the
hypotenuse, which is always opposite the right
angle.”
0 Right triangle
Obtuse triangle
0 At the website, regentsprep.org:
0 The next type of triangle is an obtuse triangle---
where one angle measures more than 90 degrees.
So, where you see one “wide mouth’ of an angle of
a triangle, you know it is an obtuse triangle.”
0 Obtuse triangle
Equiangular triangle
0 Equiangular triangle - regentsprep.org
0 Our last triangle—the equiangular triangle is
where you have equal angles and it is like our
equilateral triangle. This is a very unique triangle,
especially for balance or for structure.
0 Equiangular triangle
Practice with triangles
0 Practice with triangles on the website,
regentsprep.org
0 Let’s practice a few of these problems to review
what we learned.
Practice #1
0 Practice #1 - regentsprep.org
0 This asks what type of triangle will we get, based
on the given angles? Talk amongst your groups to
find an answer and give a reason. I will call upon
the group I choose ‘randomly.’
0 The answer is obtuse and if you click on the
explanation, it will show you.
0 Practice #1
Practice #2
0 Practice #2 – from regentsprep.org
0 This next problem is much like an Algebra
equation so when you approach the ratios, ‘1: 3: 5,’
you would see it as adding 1x to 3x to 5x to be
equal to the total amount of the insides of an
angle. Which is how many degrees?” The answer
would be 180 degrees. So, 1x+3x+5x= 180. Solve
for x.
0 Click here for an answer with an explanation.
TICKET OUT THE DOOR
0 Practice #3 - regentsprep.org
0 This last one is your ticket out the door so please
use the half sheets that I just handed out to you.
Problem #3 says, “The vertex angle of an isosceles
triangle measures eight times the measure of a
base angle. Find the measure of a base angle.”
Now how do we do this? It would help to first
draw a picture but remember which is the base
angle to the vertex angle? Next, write an equation
and work within your groups. Show the
explanation with the solution of x = 18. I will wait
for a solution. Check the site for an explanation.
In closing
0 Hopefully by now you can view triangles through
two aspects: sides and angles. As you begin your
assignment, you will be able to solve for the sides
or the angles based on what you have learned. Are
there any questions?
0 If so, please visit me during Advisory or email me
at [email protected]
References
0 Images from Microsoft and Google
0 Sound from Power Point
0 “Sides and Angles” – courtesy of regentsprep.org