Download 7th and 8th Geometry Monday-Friday Standard 6.G.A.1. Find the

7th and 8th Geometry
Monday-Friday
Standard
6.G.A.1. Find the area of right triangles, other triangles, special quadrilaterals, and polygons
by composing into rectangles or decomposing into triangles and other shapes; apply these
techniques in the context of solving real-world and mathematical problems.
Objective
SWBAT identify and classify a triangle
Vocabulary
Students will be first introduce to 3 new terms from the new vocabulary
(congruent segments, congruent angles, and right angle)
Congruent angle- line segments having the same length
Congruent angles- angles having the same length
Right triangles- a triangle with one right angle
Acute angle-a triangle with 3 acute angles
Obtuse angle- a triangle with one obtuse angle
Equilateral triangle: a triangle with three congruent sides and two congruent
angles
Isosceles triangles- a triangle with two congruent sides and two congruent
angles
Scalene triangle- a triangle with three sides of different lengths
Get Started
sections
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Problem 1 a-c: Have students look at th and ask if this angle is smaller
or greater than 90 deg? For every other angle ask why is it “name of
angle”?
start of by saying that a triangle is a three-sided figure with three
angles. How to classify an angle it’s by its angle. *State remember
when we were working with angles and how we had to classify them,
what does classify mean?
A triangle could also be classified by its lengths of its sides
Problem 2a-c: Say that we will be classifying these triangles by their
angles. For each problem teacher will have students to classify the
angles that are inside the triangle first. After classifying the angles
and count how many angles there’re then students will classify the
triangle. Have students find the sum of the interior of the angle. (this
will be the same for 2b.)
*State that every triangle measures 180deg *
2b: Same questions as 2a just switch them around. Start of by asking
students, what kind of angle measures 115deg? Have students look
Practice: Build
the concept
Try it together
at the angle from the inside of the triangle then classify it. Then have
them find similarities to a triangle. *state that every triangle only has
one obtuse triangle because the sum of the interior of the triangle
must be 180deg. so it is impossible to have 2 obtuse angles
 2c same questioning as above just with a right angle (flip questions
around)
 Problem 3a-c: Say that these triangles will be classified by the lengths
of the sides. Inform students that a way for us to classify these
triangles is by looking at the dash that’s on the two sides. The dash
on 3a means that they are the same length, or congruent. So a
triangle that has equal sides is an isosceles triangle. Also two angles
of an isosceles trig. are also congruent, which means that they have
the same measurement.
 3b: ask students how many sides of the triangle are congruent? Ask
students what symbol tells us if the sides are congruent? How many
congruent sides are there? A triangle with 3 cong. Sides is an
equilateral triangle. Therefore, because the sum of the three angles is
180deg., all three angles are congruent, each angle measurese
60deg. (add 60deg to each angle and then add them up)
 3c: What do you notice of the sides of the triangle? They are all
different lengths. What is the name of the triangle that has all
different lengths? (scalene trig.) *A triangle is named by its vertices.
The vertices of this triangle are K, L, and M. The vertices are listed in
any order. *does this look familiar? One name to name this triangle is
KLM and like always we have to use a symbol to know what we are
labeling. And the symbol is a small triangle.
Have student look at the figure in build your concept
Say: each of the interior angles in the triangle shown is shaded with a
different color.
Say: The sum of the measures of the interior angles can be found by tearing
off each angle, then fitting them together.
Direct students to the right side of the triangle
 Looking at the 3 angles on the side what angle are they forming?
 What is the measure of a straight angle?
 What is the sum of the measure of the interior angles of a triangle?
Problem 4:
 First classify this triangle by its angles
 Are any if the angles right angles?
 What kind of triangle has one right angle?
 Now, classify this triangle by its sides.
 Are any of the sides the same length? (no)
 What kind of triangle has sides with different lengths? (scalene trig.)
Problem 5:
Skills Building:
New and
Review
 What type of angle does this triangle have? (acute angle)
 What kind of triangle has three acute angles? (acute triangles)
 Describe the lengths of the sides in triangle. (they are congruent)
 What kind of triangle has three congruent sides? Equilateral triangle)
Problem 6:
 Based on its angles, what type of triangle is this? (obtuse triangle)
 Why is it obtuse? (it has one obtuse angle)
Problem 7
 What are the three different names for the triangles on problem 6?
(possible answers: DEF DFE EDF EFD FED FDE)
Problem 8
 Look at the triangle. What type of triangle is this?
 Obtuse, why is it an obtuse triangle?
Problem 9
 How many acute angles does this triangle have?
 What type of triangle has 3 acute angles?
Problem 10
 Are there any right angels in their triangle?
 What triangle has a right angle?
Problem 11
 What type of triangle has 2 congruent sides?
 How could you tell these are congruent to each other?
Problem 12
 Does this triangle have congruent sides?
 How many congruent sides does this triangle have?
 But this triangle doesn’t have the slash marks, so how are you able to
tell the 3 sides are congruent?
Problem 13
 Based on its lengths what type of triangle is this?
 Why is it an isosceles triangle?
Problem 14
 What type of triangle is number 11? It’s an isosceles triangle
 An isosceles has how many congruent sides?
 How many congruent angles does this isosceles triangle have?
 Two angles of an isosceles triangle are congruent, which means they
have the same measurement.
Problem 15
 What type of triangle is number 12?
 How many equal sides does an equilateral triangle have?
 What does this tell us about the angles? (they are congruent) Equal
sides means congruent angels
 What is the interior sum of a triangle?
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Using Logical
Thinking
We know that the total sum of the inside of a triangle is 180deg, but
how do we get 180deg?
By adding up all the angles measurements
How many angles are we going to be solving for? (3)
We need to find the angel measurement of each angle
So how many angles are we going to solve for?
You know two things, you know the total sum is 180deg and you
know that you need to find the measurements of 3 angels.
What operations are we going to use the find the sum of each angel?
Remember that we need to split the total sum into equal groups.
You are going to divide
Dived 180/3
What is the answer? 60deg
So what is the measurement of each angle?
Each angle will be 60deg
Read question out loud
Draw Tyler’s triangle on the board
Have everyone draw an obtuse triangle
a. Find the type of triangle
1. What was the degree of the angel that Tyler drew? More than
90deg
2. Ask students: What triangle has one obtuse angle?
b. How?
1. Does Tyler’s triangle have any congruent sides? No
c. What information is given?
i. Have two students answer these two fill in the blanks
2. The triangle has (3) sides with different lengths.
3. There is (1) angle with a measure greater than 90deg.
d. Solve:
1. An isosceles triangle has (2) sides with the same length.
2. Did Tyler draw an isosceles triangle? (no)
3. By looking at the word problem how do you know it’s a
scalene triangle? (three different lengths)
4. Using the information the word problem gave us what type of
angle did Tyler drew a (obtuse). Again what type of triangle
has one obtuse angel? (obtuse triangle)
5. Tyler drew a (scalene, obtuse) triangle
e. Explain:
1. An isosceles triangle has two sides with the same length.
Tyler’s triangle has no sides with the same length.
ProblemSolving: New
and Review
Check up
Problem 16:
Read question out loud
Ask students who agrees with Fiona?
Ask students who disagrees with Fiona?
Ask students to write down their explanation
-Yes, an equilateral triangle has three sides with the same length, and Fiona’s
triangle has three sides with the same length.
Problem 17:
Classy the green triangle by its sides
Does this triangle have any congruent sides? No
What type of triangle has no congruent sides? Scalene
Problem 18
Classify the purple triangle by the angle that contains the star. Write acute,
right, or obtuse. (Acute)
-What is the question we ask ourselves when we are classifying angels?
-Is it smaller or greater than 90deg? smaller
What type of angle is smaller than 90deg? acute
Problem 19
Have students work independently first
Give students 8 minutes to answer
Pair students up and have them share their answer
Gather students attention
Ask one group to share and explain their answer
Why can’t Henrietta draw a triangle with those measurements?
What is the total interior sum of a triangle? 180deg
What is the total sum of the degrees from problem 19? 200deg
-No, the sum of the angle that Henrietta wants to use is more than 180deg.
It would be impossible to draw such a triangle.