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5-1 Classifying Triangles
Today we will be learning how to classify triangles according to length of sides and measurement of the angles.
First we will learn to classify by the
ANGLES
Right triangles have ONE right angle
Acute Triangles have three acute angles
Smaller than 90o
Smaller than 90o
Smaller than 90o
Acute Angle
Obtuse Triangles have ONE obtuse angle
Obtuse Angle
We will now learn to classify triangles by their sides.
If you collapsed all of the sides they would form a line.
Equilateral Triangles have 3 equal sides
Isosceles Triangles have 2 equal sides.
Scalene Triangles have NO equal sides.
Classifying Triangles by Their Sides EQUILATERAL – 3 congruent sides
ISOSCELES – at least two sides
congruent
SCALENE – no sides congruent
EQUILATERAL
ISOSCELES
SCALENE
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
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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You have now learned that triangles can be classified by either their sides or their angles.
5-2 ANGLES OF A TRIANGLE
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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
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
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°.°
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