Transcript Geom_CH 4_Sect 1

4-1
4-1 Classifying
ClassifyingTriangles
Triangles
Warm Up
Lesson Presentation
Lesson Quiz
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Holt Geometry
Geometry
4-1 Classifying Triangles
Warm Up
Classify each angle as acute, obtuse, or right.
1.
3.
right
2.
acute
obtuse
4. If the perimeter is 47, find x and the lengths
of the three sides.
x = 5; 8; 16; 23
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4-1 Classifying Triangles
Objectives
Classify triangles by their angle measures
and side lengths.
Use triangle classification to find angle
measures and side lengths.
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4-1 Classifying Triangles
Vocabulary
acute triangle
equiangular triangle
right triangle
obtuse triangle
equilateral triangle
isosceles triangle
scalene triangle
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4-1 Classifying Triangles
Recall that a triangle ( ) is a polygon
with three sides. Triangles can be
classified in two ways: by their angle
measures or by their side lengths.
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4-1 Classifying Triangles
C
A
B
AB, BC, and AC are the sides of
A, B, C are the triangle's vertices.
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ABC.
4-1 Classifying Triangles
Triangle Classification By Angle Measures
Acute Triangle
Three acute angles
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4-1 Classifying Triangles
Triangle Classification By Angle Measures
Equiangular Triangle
Three congruent acute angles
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4-1 Classifying Triangles
Triangle Classification By Angle Measures
Right Triangle
One right angle
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4-1 Classifying Triangles
Triangle Classification By Angle Measures
Obtuse Triangle
One obtuse angle
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4-1 Classifying Triangles
Class Example: Classifying Triangles by Angle
Measures
Classify
BDC by its angle measures.
B is an obtuse angle.
B is an obtuse angle. So
triangle.
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BDC is an obtuse
4-1 Classifying Triangles
Class Example: Classifying Triangles by Angle
Measures
Classify
ABD by its angle measures.
ABD and CBD form a linear pair, so they are
supplementary.
Therefore mABD + mCBD = 180°. By substitution,
mABD + 100° = 180°. So mABD = 80°. ABD is an
acute triangle by definition.
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4-1 Classifying Triangles
Example 1 - 3
Classify
measure
EHG,
EFH,
Triangle EHG is right
Triangle EFH is obtuse
Triangle FHG is equiangular
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FHG by its angle
4-1 Classifying Triangles
Triangle Classification By Side Lengths
Equilateral Triangle
Three congruent sides
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4-1 Classifying Triangles
Triangle Classification By Side Lengths
Isosceles Triangle
At least two congruent sides
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4-1 Classifying Triangles
Triangle Classification By Side Lengths
Scalene Triangle
No congruent sides
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4-1 Classifying Triangles
Remember!
When you look at a figure, you cannot assume
segments are congruent based on appearance.
They must be marked as congruent.
Holt Geometry
4-1 Classifying Triangles
Class Example: Classifying Triangles by Side Lengths
Classify
EHF by its side lengths.
From the figure,
isosceles.
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. So HF = 10, and
EHF is
4-1 Classifying Triangles
Class Example: Classifying Triangles by Side Lengths
Classify
EHG by its side lengths.
By the Segment Addition Postulate, EG = EF + FG =
10 + 4 = 14. Since no sides are congruent, EHG
is scalene.
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4-1 Classifying Triangles
Example # 1 - 3
Classify
lengths.
ABC,
ABD and
ABC = equilateral
Triangle ABD = Scalene
Triangle ACD = scalene
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ACD by its side
4-1 Classifying Triangles
Example # 1: Using Triangle Classification
Find the side lengths of
Step 1 Find the value of x.
JK = KL
4x – 1.3 = x + 3.2
3x = 4.5
x = 1.5
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JKL.
4-1 Classifying Triangles
Example #1 Continued
Find the side lengths of
Step 2 Substitute 1.5 into
the expressions to find the
side lengths.
JK = 4x – 1.3
= 4(1.5) – 1.3 = 4.7
KL = x + 3.2
= 1(1.5) + 3.2 = 4.7
JL = 5x + 0.2
= 5(1.5) +0.2 = 7.3
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JKL.
4-1 Classifying Triangles
Example # 2
Find the side lengths of equilateral
FGH.
Step 1 Find the value of y.
Given.
FG = GH = FH
Def. of  segs.
Substitute
3y – 4 = 2y + 3 (3y – 4) for FG and
(2y + 3) for GH.
y=7
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Add 4 and subtract
2y from both sides.
4-1 Classifying Triangles
Check It Out! Example #2 Continued
Find the side lengths of equilateral
FGH.
Step 2 Substitute 7 into the expressions to find the
side lengths.
FG = 3y – 4
= 3(7) – 4 = 17
GH = 2y + 3
= 2(7) + 3 = 17
FH = 5y – 18
= 5(7) – 18 = 17
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4-1 Classifying Triangles
Homework:
Page 219: # 1-19
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4-1 Classifying Triangles
Exit Question
Classify each triangle by its angles and sides.
1.
MNQ acute; equilateral
2.
NQP obtuse; scalene
3.
MNP acute; scalene
4. Find the side lengths of the triangle.
29; 29; 23
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4-1 Classifying Triangles
Exit Question
Name:
Classify each triangle by its angles and sides.
1.
MNQ
2.
NQP
3.
MNP
4. Find the side lengths of the triangle.
Holt Geometry
4-1 Classifying Triangles
Exit Question
Name:
Classify each triangle by its angles and sides.
1.
MNQ
2.
NQP
3.
MNP
4. Find the side lengths of the triangle.
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