Transcript Presentation: 5-1 & 5

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 Angle
Acute
Triangles
have three
acute angles
Smaller than 90o
Smaller than 90o
Smaller than 90o
Obtuse Angle
Obtuse
Triangles
have ONE
obtuse angle
We will now learn
to classify triangles
by their sides.
Equilateral
Triangles
have 3 equal
sides
If you collapsed
all of the sides
they would
form a line.
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
EQUILATERAL
ISOSCELES
 SCALENE – no sides congruent
SCALENE
Classifying Triangles by Their Angles
 EQUIANGULAR – all angles are congruent
 ACUTE – all angles are acute
 RIGHT – one right angle
ACUTE
EQUIANGULAR
 OBTUSE – one obtuse angle
RIGHT
OBTUSE
Can You Classify the Different Triangles in
the Picture Below?
 Triangle AED = Equilateral, Equiangular
 Triangle ABC = Equilateral, Equiangular
 Triangle ACD = Isosceles, Obtuse
 Triangle ACE = Scalene, Right
Classify the following triangles: AED, ABC, ACD, ACE
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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
Find m JKM.
SOLUTION
STEP 1 Write and solve an equation to find the value
of x.
(2x – 5)° = 70° + x°
x = 75
Apply the Exterior Angle Theorem.
Solve for x.
STEP 2 Substitute 75 for x in 2x – 5 to find m JKM.
2x – 5 = 2 75 – 5 = 145
ANSWER The measure of  JKM is 145°.
GUIDED PRACTICE
for Examples 3 and 4
3. Find the measure of
1 in the diagram shown.
ANSWER The measure of  1 in the diagram is 65°.
GUIDED PRACTICE
for Examples 3 and 4
4. Find the measure of each interior angle of
ABC,
where m A = x ° , m B = 2x° , and m C = 3x°.
SOLUTION
A+ B+
x
C = 180°
x + 2x + 3x = 180°
6x = 180°
x = 30°
B = 2x = 2(30) = 60°
C = 3x = 3(30) = 90°
2x
3x
GUIDED PRACTICE
for Examples 3 and 4
5. Find the measures of the acute
angles of the right triangle in
the diagram shown.
ANSWER
26° and 64°