5-1 Classifying Triangles Today we will be learning how to classify triangles according to length of...
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![Page 1: 5-1 Classifying Triangles Today we will be learning how to classify triangles according to length of sides and measurement of the angles.](https://reader031.fdocuments.in/reader031/viewer/2022013012/56649e865503460f94b8a196/html5/thumbnails/1.jpg)
5-1 Classifying Triangles
![Page 2: 5-1 Classifying Triangles Today we will be learning how to classify triangles according to length of sides and measurement of the angles.](https://reader031.fdocuments.in/reader031/viewer/2022013012/56649e865503460f94b8a196/html5/thumbnails/2.jpg)
Today we will be learning how to classify triangles according to length of sides and measurement of the angles.
![Page 3: 5-1 Classifying Triangles Today we will be learning how to classify triangles according to length of sides and measurement of the angles.](https://reader031.fdocuments.in/reader031/viewer/2022013012/56649e865503460f94b8a196/html5/thumbnails/3.jpg)
First we will learn to classify by the
ANGLES
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Right triangles have ONE right angle
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Acute Triangles have three acute angles
Smaller than 90o
Smaller than 90o
Smaller than 90o
Acute Angle
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Obtuse Triangles have ONE obtuse angle
Obtuse Angle
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We will now learn to classify triangles by their sides.
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If you collapsed all of the sides they would form a line.
Equilateral Triangles have 3 equal sides
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Isosceles Triangles have 2 equal sides.
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Scalene Triangles have NO equal sides.
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Classifying Triangles by Their Sides EQUILATERAL – 3 congruent sides
ISOSCELES – at least two sides
congruent
SCALENE – no sides congruent
EQUILATERAL
ISOSCELES
SCALENE
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Classifying Triangles by Their Angles EQUIANGULAR – all angles are congruent
ACUTE – all angles are acute
RIGHT – one right angle
OBTUSE – one obtuse angle
EQUIANGULARACUTE
RIGHT
OBTUSE
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Can You Classify the Different Triangles in the Picture Below?
Classify the following triangles: AED, ABC, ACD, ACE
Triangle AED = Equilateral, Equiangular
Triangle ABC = Equilateral, Equiangular
Triangle ACD = Isosceles, Obtuse
Triangle ACE = Scalene, Right
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Slide 3 of 3
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Slide 3 of 3
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Slide 3 of 3
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Slide 3 of 3
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You have now learned that triangles can be classified by either their sides or their angles.
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5-2 ANGLES OF A TRIANGLE
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Slide 1 of 2
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Slide 2 of 2
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Slide 2 of 2
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Slide 2 of 2
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Slide 2 of 2
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Slide 2 of 2
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Slide 2 of 2
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Slide 2 of 2
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Slide 2 of 2
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Slide 2 of 2
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Slide 2 of 2
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Slide 2 of 2
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Slide 2 of 2
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Slide 2 of 2
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EXAMPLE 3 Find an angle measure
SOLUTION
STEP 1 Write and solve an equation to find the value of x.
Apply the Exterior Angle Theorem.(2x – 5)° = 70° + x°
Solve for x.x = 75
STEP 2Substitute 75 for x in 2x – 5 to find m∠JKM.
2x – 5 = 2 75 – 5 = 145
Find m∠JKM.
The measure of ∠JKM is 145°.ANSWER
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GUIDED PRACTICE for Examples 3 and 4
Find the measure of 1 in the diagram shown.3.
The measure of ∠1 in the diagram is 65°.ANSWER
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GUIDED PRACTICE for Examples 3 and 4
SOLUTION
A + B + C = 180°
x + 2x + 3x = 180°
6x = 180°
x = 30°
B = 2x = 2(30) = 60°
C = 3x = 3(30) = 90°
x
2x 3x
4. Find the measure of each interior angle of ABC, where m A = x , m B = 2x° , and m C = 3x°.°
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GUIDED PRACTICE for Examples 3 and 4
5. Find the measures of the acute angles of the right triangle in the diagram shown.
26° and 64°ANSWER