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Classifying Triangles
LESSON 4–1
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Five-Minute Check (over Chapter 3)
TEKS
Then/Now
New Vocabulary
Key Concept: Classifications of Triangles by Angles
Example 1: Classify Triangles by Angles
Example 2: Classify Triangles by Angles Within Figures
Key Concept: Classifications of Triangles by Sides
Example 3: Real-World Example: Classify Triangles by Sides
Example 4: Classify Triangles by Sides Within Figures
Example 5: Finding Missing Values
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Over Chapter 3
A. consecutive interior angles
B. corresponding angles
C. complementary angles
D. supplementary
What is the special name given to the pair of angles shown by 2 and 6?
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Over Chapter 3
A. 118
B. 108
C. 62
D. 52
Find m3.
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Over Chapter 3
A. 118
B. 108
C. 72
D. 62
Find m4.
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Over Chapter 3
Find the slope of the line that contains the points at (4, 4) and (2, –5).
A.
B.
C.
D.
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Over Chapter 3
A.
B.
C.
D.
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Targeted TEKS
G.5(A) Investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles,diagonals of quadrilaterals, interior and exterior anglesof polygons, and special segments and angles ofcircles choosing from
Mathematical ProcessesG.1(A), G.1(C)
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You measured and classified angles.
• Identify and classify triangles by angle measures.
• Identify and classify triangles by side measures.
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• acute triangle
• equiangular triangle
• obtuse triangle
• right triangle
• equilateral triangle
• isosceles triangle
• scalene triangle
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Classify Triangles by Angles
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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Classify Triangles by Angles
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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A. acute
B. equiangular
C. obtuse
D. right
B. ARCHITECTURE The frame of this window design is made up of many triangles. Classify ΔADE.
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Classify Triangles by Angles Within Figures
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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A. acute
B. equiangular
C. obtuse
D. right
Classify ΔACD as acute, equiangular, obtuse, or right.
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Classify Triangles by Sides
ARCHITECTURE The triangle truss shown is modeled for steel construction. Classify ΔJMN, ΔJKO, and ΔOLN as acute, obtuse, or right.
Answer: ΔJMN is obtuse. ΔJKO is right. ΔOLN is equiangular.
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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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Classify Triangles by Sides Within Figures
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.
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Classify Triangles by Sides Within Figures
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 BD, classify ΔABC as equilateral, isosceles, or scalene.
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Finding Missing Values
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.
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Finding Missing Values
Answer: KM = ML = 7, KL = 11
Step 2 Substitute to find the length of each side.
KM = 4d – 13 Given
= 4(5) – 13 or 7 d = 5
ML = KM Given
= 7 KM = 7
KL = d + 6 Given
= 5 + 6 or 11 d = 5
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ALGEBRA Find x and the measure of each side of equilateral triangle ABC if AB = 6x – 8, BC = 7 + x, and AC = 13 – x.
A. x = 10; all sides are 3.
B. x = 6; all sides are 13.
C. x = 3; all sides are 10.
D. x = 3; all sides are 16.
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Classifying Triangles
LESSON 4–1