A triangle can be classified by _________ and __________. sidesangles There are four ways to...
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![Page 1: A triangle can be classified by _________ and __________. sidesangles There are four ways to classify triangles by angles. They are Equiangular Acute.](https://reader035.fdocuments.net/reader035/viewer/2022062518/56649e745503460f94b73f87/html5/thumbnails/1.jpg)
![Page 2: A triangle can be classified by _________ and __________. sidesangles There are four ways to classify triangles by angles. They are Equiangular Acute.](https://reader035.fdocuments.net/reader035/viewer/2022062518/56649e745503460f94b73f87/html5/thumbnails/2.jpg)
A triangle can be classified by _________ and __________.sides angles
There are four ways to classify triangles by angles. They are
EquiangularAcuteObtuseRight
All angles congruent3 acute angles1 obtuse and two acute angles1 right and two acute angles
There are three ways to classify triangles by sides. They are
Equilateral - 3 congruent sides and anglesIsosceles - 2 congruent sides and anglesScalene - no congruent sides or angles
![Page 3: A triangle can be classified by _________ and __________. sidesangles There are four ways to classify triangles by angles. They are Equiangular Acute.](https://reader035.fdocuments.net/reader035/viewer/2022062518/56649e745503460f94b73f87/html5/thumbnails/3.jpg)
Let’s take a closer look at the isosceles triangle:
The two congruent sides are called legs.
LEG LEG
The other side is called the base.
BASE
The two congruent angles are called the base angles.
The other angle is called the vertex angle.
VERTEX ANGLE
BASE ANGLES
![Page 4: A triangle can be classified by _________ and __________. sidesangles There are four ways to classify triangles by angles. They are Equiangular Acute.](https://reader035.fdocuments.net/reader035/viewer/2022062518/56649e745503460f94b73f87/html5/thumbnails/4.jpg)
WHITE NOTE CARD:
Isosceles Triangle
LEG LEG
BASE
VERTEX ANGLE
BASE ANGLES
The legs and base angles are congruent.
Vertex angles is always opposite the base.
![Page 5: A triangle can be classified by _________ and __________. sidesangles There are four ways to classify triangles by angles. They are Equiangular Acute.](https://reader035.fdocuments.net/reader035/viewer/2022062518/56649e745503460f94b73f87/html5/thumbnails/5.jpg)
REVIEW:
RIGHT TRIANGLE
LEG
LEG
HYPOTENUSE
![Page 6: A triangle can be classified by _________ and __________. sidesangles There are four ways to classify triangles by angles. They are Equiangular Acute.](https://reader035.fdocuments.net/reader035/viewer/2022062518/56649e745503460f94b73f87/html5/thumbnails/6.jpg)
Angle Sum Theorem
What is the sum of the measures of the angles in a triangle?
Is this true for all triangles? Even the really big ones and really small ones?
Proof of Angle Sum Theorem
![Page 7: A triangle can be classified by _________ and __________. sidesangles There are four ways to classify triangles by angles. They are Equiangular Acute.](https://reader035.fdocuments.net/reader035/viewer/2022062518/56649e745503460f94b73f87/html5/thumbnails/7.jpg)
Remember the proof of the Triangle Sum Theorem? Good stuff!
Given: ABC is a triangle.
A
B
C
(Number the angles for convenience)
1
2
3
Prove: 1 + 2 + 3 = 180
STATEMENTS REASONS
1. ABC is a triangle 1. Given
2. Draw a line through B that is parallel to AC
2. Parallel Postulate
3. 4 + 2 + 5 = 180
4. 1 4 and 3 5
5. 1 + 2 + 3 = 180
4. If two parallel lines are cut by a transversal then the alternate interior angles are congruent.
5. Substitution Property
4 5
3. Definition of Supplementary angles
Click on the reasonfor an explanation.
![Page 8: A triangle can be classified by _________ and __________. sidesangles There are four ways to classify triangles by angles. They are Equiangular Acute.](https://reader035.fdocuments.net/reader035/viewer/2022062518/56649e745503460f94b73f87/html5/thumbnails/8.jpg)
![Page 9: A triangle can be classified by _________ and __________. sidesangles There are four ways to classify triangles by angles. They are Equiangular Acute.](https://reader035.fdocuments.net/reader035/viewer/2022062518/56649e745503460f94b73f87/html5/thumbnails/9.jpg)
An exterior angle is formed by one side of a triangle and the extension of another side.
Exterior angle
Exterior angle
Exterior angle
![Page 10: A triangle can be classified by _________ and __________. sidesangles There are four ways to classify triangles by angles. They are Equiangular Acute.](https://reader035.fdocuments.net/reader035/viewer/2022062518/56649e745503460f94b73f87/html5/thumbnails/10.jpg)
Interior angles
Remote interior angles are the interior angles in the triangle that are not adjacent to the exterior angle.
Exterior angle
remote interior angles
Exterior angle
Exterior angle
![Page 11: A triangle can be classified by _________ and __________. sidesangles There are four ways to classify triangles by angles. They are Equiangular Acute.](https://reader035.fdocuments.net/reader035/viewer/2022062518/56649e745503460f94b73f87/html5/thumbnails/11.jpg)
Exterior Angle Theorem
The measure of an exterior angle is equal to the sum of the measures of the two remote interior angles.
Exterior angle
Remote interior angles
41
2
In other words, 4 = 1 + 2.
![Page 12: A triangle can be classified by _________ and __________. sidesangles There are four ways to classify triangles by angles. They are Equiangular Acute.](https://reader035.fdocuments.net/reader035/viewer/2022062518/56649e745503460f94b73f87/html5/thumbnails/12.jpg)
Add this proof to page 37 that already has the Triangle Sum Theorem proof.
What could be more fun than
another proof? I can’t wait!
![Page 13: A triangle can be classified by _________ and __________. sidesangles There are four ways to classify triangles by angles. They are Equiangular Acute.](https://reader035.fdocuments.net/reader035/viewer/2022062518/56649e745503460f94b73f87/html5/thumbnails/13.jpg)
Given: ABC is a triangle with exterior angle 4
A
B
C
1
2
3 4
Prove: 1 + 2 = 4
(The sum of the measures of the two remote interior angles in a triangle is equalto the measure of the exterior angle)
STATEMENTS REASONS
1. ABC is a triangle with exterior angle 4
2. 1 + 2 + 3 = 180
3. 3 + 4 = 180
4. 1 + 2 + 3 = 3 + 4
5. 1 + 2 = 4
1. Given
2. Triangle Sum Theorem
3. Definition of Linear Pair
4. Substitution Property
5. Subtraction Property
1 + 2 + 3 = 180
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Add the Exterior Angle Theorem to your Triangle Sum Theorem note card (it’s a colored one).
Triangle Sum Theorem
The sum of the measures of the angles in a triangle is 180.
Exterior Angle Theorem
The measure of an exterior angle is equal to the sum of the measures of the two remote interior angles.
4
2
1
4 = 1 + 2
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Proofs are awesome! I
hope we get to do more of them
soon!
I’m sure we will!
Geometry is super!
I love math! It’s
everywhere!
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