4-1 Classifying Triangles You measured and classified angles. Identify and classify triangles by...
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![Page 1: 4-1 Classifying Triangles You measured and classified angles. Identify and classify triangles by angle measures. Identify and classify triangles by side.](https://reader036.fdocuments.net/reader036/viewer/2022062409/56649f4c5503460f94c6cdab/html5/thumbnails/1.jpg)
4-1 Classifying Triangles
You measured and classified angles.
• Identify and classify triangles by angle measures.
• Identify and classify triangles by side measures.
![Page 2: 4-1 Classifying Triangles You measured and classified angles. Identify and classify triangles by angle measures. Identify and classify triangles by side.](https://reader036.fdocuments.net/reader036/viewer/2022062409/56649f4c5503460f94c6cdab/html5/thumbnails/2.jpg)
DefinitionA triangle is a figure formed by
three line segments that connect three noncollinear points.
Side
Side
Side
vertex
vertex
vertexA B
C
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Naming a triangleA triangle is named using its vertices and
a ∆ symbol. This triangle can be named ∆ ABC
A B
C
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Classifying Triangles
• Triangles can be classified in two ways – by their angles or by their sides.
• All triangles have at least two acute angles, but the third angles is used to classify the triangle.
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Triangle Classification by Angles
Acute3 acute angles
.Obtuse
One obtuse angle.
Right
One right angle. Equiangular
3 congruent acute angles.
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A. Classify the triangle as acute, equiangular, obtuse, or right.
Answer: The triangle has three congruent angles. It is an equiangular triangle.
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B. Classify the triangle as acute, equiangular, obtuse, or right.
Answer: One angle of the triangle measures 130°, so it is an obtuse angle. The triangle has an obtuse angle, so it is an obtuse triangle.
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A. acute
B. equiangular
C. obtuse
D. right
A. ARCHITECTURE The frame of this window design is made up of many triangles. Classify ΔACD.
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Point W is in the interior of XYZ, so by the Angle Addition Postulate, mXYW + mWYZ = mXYZ. By substitution, mXYZ = 40 + 50 = 90.
Answer: Since ΔXYZ has a right angle, it is a right triangle.
Classify ΔXYZ as acute, equiangular, obtuse, or right. Explain your reasoning.
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Triangle Classification by Sides
Scaleneno sides congruent.
Isosceles
two sides congruent.
Equilateral
All sides congruent.
A
B
C
D
E
F
G
H
I
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Try ItClassify each triangle using both
angle and side classification.
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ARCHITECTURE The triangle truss shown is modeled for steel construction. Classify ΔJMN, ΔJKO, and ΔOLN as equilateral, isosceles, or scalene.
Answer: ΔJMN has no congruent sides, so it is a scalene triangle. ΔJKO has no congruent sides, so it is a scalene triangle. ΔOLN has all sides congruent, so it is an equilateral triangle.
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A. isosceles
B. equilateral
C. scalene
D. right
ARCHITECTURE The frame of this window design is made up of many triangles. Classify ΔABC.
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By the definition of midpoint, VY = YX.
VY + YX = VX Segment Addition Postulate
VY + VY = 8.4 Substitution
2VY = 8.4 Simplify.
VY = 4.2 Divide each side by 2.
If point Y is the midpoint of VX, and WY = 3.0 units, classify ΔVWY as equilateral, isosceles, or scalene. Explain your reasoning.
So, VW = 4.5 units, WY = 3.0 units, and VY = 4.2 units.
Answer: Since all three sides have different lengths, the triangle is scalene.
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A. equilateral
B. isosceles
C. scalene
If point C is the midpoint of , classify ΔABC as equilateral, isosceles, or scalene.
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Step 1 Find d.
ALGEBRA Find the measures of the sides of isosceles triangle KLM with base KL.
__
KM = ML Given
4d – 13 = 12 – d Substitution
5d – 13 = 12 Add d to each side.
5d = 25 Add 13 to each side.
d = 5 Divide each side by 5.
Answer: KM = ML = 7, KL = 11
Step 2 Substitute to find the length of each side.
KM = 4d – 13 Given = 5 + 6 or 11 d = 5
= 4(5) – 13 or 7 d = 5
ML = KM Given
= 7 KM = 7
KL = d + 6 Given
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• What is a triangle?
A figure formed by three line segments that connect three noncollinear points.
• What is the sum of the measures of the interior of any triangle?
The sum of the measures of the angles of a triangle is 180°
• How are triangles classified and named?
Triangles are classified by sides and angles.
Sides: scalene, isosceles and equilateral.
Angles: acute, obtuse, right and equiangular.
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4-1 Assignment
Page 240, 15 -20, 22-36 even, 40 - 42