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
Slide 4
Angles and Triangles As youve 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. www.regentsprep.org
http://www.regentsprep.org/Regents/math/geome try/GP5
Slide 5
Sides of Triangles 0 Accessing the www.regentsprep.org to go to
the Geometry section, the sides of triangles.www.regentsprep.org 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.
Slide 6
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 Ill choose a group for an
answer. (Ans: equal) Remember that term for the next slide.
Slide 7
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.www.regentsprep.org Please continue and click to view the
isosceles triangle.
http://www.regentsprep.org/Regents/math/geometry /GP5/
Slide 8
Equilateral triangle 0 From the website, www.regentsprep.org,
we are looking at the sides of triangles.www.regentsprep.org 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
http://www.regentsprep.org/Regents/math/geo
metry/GP5/LTriangle.htm
Slide 9
Angles of triangles 0 At the website, www.regentsprep.org,
discussing the angles of a triangle.www.regentsprep.org 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
www.regentsprep.org/Regents/math/geometry/a ngles
Slide 10
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 Acute triangle
Slide 11
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 Right triangle
Slide 12
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
Obtuse triangle
Slide 13
Equiangular triangle 0 Equiangular triangle - regentsprep.org 0
Our last trianglethe 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 Equiangular triangle
Slide 14
Practice with triangles 0 Practice with triangles on the
website, regentsprep.org 0 Lets practice a few of these problems to
review what we learned.
Slide 15
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 #1
Slide 16
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. Click
here for an answer with an explanation
Slide 17
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.Check
the site for an explanation
Slide 18
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]@phoenixunion.org
Slide 19
References 0 Images from Microsoft and Google 0 Sound from
Power Point 0 Sides and Angles courtesy of regentsprep.org