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Types of Angles
Class: Geometry
Grade Level: 9th
Unit: Triangles (2)
Teacher: Ms. Jamie Davis
Common Core State Standards (CCSS)
CCSS.Math.Content.HSG-MG.A.1 Use geometric shapes, their measures, and their
properties to describe objects
Iowa Core Curriculum-Subject Area Standard(s)
geometry: understands and applies properties and relationships of geometric figures;
representation: creates and uses representations to organize, record, and communicate
mathematical ideas
connections- recognizes and uses connections among mathematical ideas and how they
build on one another to produce a coherent whole
communication- organizes and consolidates his/her mathematical thinking through
communication
representation- creates and uses representations to organize, record, and communicate
mathematical ideas
21st Century Skill(s)
Information literacy- access and evaluate information; use and manage information
Productivity and accountability- manage products and produce results
Objectives
Students will be able to recognize triangles based on their features.
Students will also be able to distinguish between key characteristics of angles and lengths
of sides.
Essential Question
Can I accurately evaluate triangles and identify them based on their properties?
Can I produce my own triangle and describe what its characteristics are?
Anticipatory Set


Yesterday we talked about triangles in regards to the length of their sides. We
identified scalene, isosceles, and equilateral triangles.
Who can draw a scalene triangle on the board and describe it? Another volunteer
for isosceles and equilateral triangles.
Today we will be talking about the angles of triangles and how they define the
type of triangle they are as well.
Teaching: Activities
Acute Triangles:
What are acute triangles?
-all angles are less than 90*
-make pun about “a-cute” like “a cute little puppy” emphasizing the little (like less than
90 being little)
Show examples:
Obtuse Triangles:
What are obtuse triangles?
-one angle is greater than 90*
-Why can’t more than one angle be more than 90*?
--angles add up to 180, 90+90=180, which wouldn’t leave an angle for the 3rd triangle, ie:
impossible
vocabulary: obtuse=big, fat; the angle is wider than 90*
show examples
Right Triangles:
What is a right triangle?
-one angle is 90*
once again, why can’t more than one angle be 90*?
-- 90+90=180, sum of triangle’s angles = 180, not more than 180
what is special about a right triangle?
Where do we see right triangles? (pretty much any corner = 90)
how do we label the sides of a right triangle? A,b,c sides where c is always the
hypotenuse side
vocabulary: hypotenuse: the side opposite of the right angle, always the longest side
(z=c, x=b, y=a)
Something special about right triangles is that you can calculate the length of a
side if you already know the length of the other two. This is why it’s important to
know which side is the hypotenuse. We can do this by using the Pythagorean
Theorem.
Pythagorean Theorem: a^2 + b^2 = c^2
Applied:
1^2+1^2=c^2, 2= c^2, sqrt(2)=c
1^2+sqrt(3)^2=c^2 1+3=c^2 4=c^2 c=2
Never fear! We’ll go over this more in a later class, this is just to introduce the
topic!
Recap:
Watch: http://www.youtube.com/watch?v=Uxk60HWQCE&playnext=1&list=PLD6A4ED54B2909A52&feature=results_main
Then briefly go over the triangles again before moving on.
Closure
On a piece of paper, draw a right triangle, obtuse triangle, acute triangle, equilateral,
isosceles, and scalene triangle. Be sure to mark what makes it specifically that. Hand in
on your way out the door.
Independent Practice
Each student is assigned two shapes (figured out in advance) based on their
understanding from the previous lesson on triangles and where they are at (below, on, or
above-target).
code: below target= and
on target=
and
above target= and
Purpose: Complete 3 of the tasks using the shapes that you are assigned and you must use
at least one of both shapes.
What’s not completed during class time is to be done at home as homework
**See below for attached table of shapes/activities relating.
Assessment
assess their understanding as they work on the shape choices activity
Materials
Tape, scissors, paper, pencils
Duration
Anticipatory set: 10 minutes
Teaching Activities: 30 minutes
Independent practice/assessment: 45 minutes
Closure: 5 minutes
Modified from Madeline Hunters Lesson Plan Design
Create a house using only
right triangles, being sure to
mark the length of the sides
and the roof must consist of at
least 4 triangles. What is the
total height of your building?
Research other defining
characteristics of triangles and
how they apply to what we’ve
already learned.
State everything that you can
identify about each triangle:
Now do the same using only
obtuse triangles with a total
length of one side of the roof
being 25 and the height up
until the roof is 100.
Looking around the
classroom, find at least 5
obtuse angles, 5 right angles,
and 5 acute angles that you
can find.
Design 4 different triangles,
assigning two of their lengths.
Use the Pythagorean Thm to
solve for the 3rd side. Find
someone else in the class that
did this choice to exchange
triangles and to try and solve
for the 3rd side using the
Pythagorean Thm as well and
see if you both came up with
the same answers. Note: what
type of triangles do these have
to be?
Draw a right, obtuse, and
acute triangle. Tear each
triangle into 3 parts and line
the angles up together. Tape
together onto another piece of
paper. What do you notice
about the angles?
Create a Venn-Diagram
comparing each type of
triangle
State two occupations that
would need to
know/understand triangles on
a regular basis and why they
would.
Find the length of the missing
side using Pythagorean’s
Theorem.
Mark each sides’ congruency if it is and
label which kind of triangle it is:
Research Pythagoras and write a short
(2 page) essay describing how he came
across his Theorem, when he did, and
any other information you are able to
provide.
Identify each type of triangle:
1)
3)
4)
5)
6)
2)
ANSWER KEY
N/A- answers may vary
Answers may vary
the angles form a line
because angles add up to
180
examples: architect,
engineer, construction
worker, artist, etc.
Answers vary depending
upon which other features
they researched.
Answers vary depending
upon what the lengths are
for the given sides that they
draw.
Venn-diagram
F1=10
F2=5
F3=6
F4=3
F1- right, isosceles
F2- acute, isosceles
F3- obtuse, scalene
I- acute, scalene
II- right, 2 sides congruent,
isosceles
III- obtuse, scalene
IV- obtuse, scalene
2 page paper
1 equilateral, acute
2 right, scalene
3 isosceles, obtuse
4 equilateral, scalene
5 isosceles, right
6 acute, obtuse