classifying triangles and angles in triangles book section ...€¦ · triangles and classification...
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Geometry CP, Oct 25
Classifying Triangles and Angles in Triangles
Book Section: 4-1 & 4-2
Essential Question: How are triangles classified and how are angles in
triangles related?
Standards: G-1.2, G-1.3, G-1.5, G-1.7, G-1.8
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Triangles and Classification
• Triangle – A three sided polygon.
• Classifying Triangles
By Angle
By Sides
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Classifying by Angles
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Examples
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Example 1A 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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Example 1B 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
Classify ΔACD as acute, equiangular, obtuse, or right.
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Classifying by Sides
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Example 3 Classify Triangles by Sides
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. equilateral
B. isosceles
C. scalene
If point C is the midpoint of BD, classify ΔABC as equilateral, isosceles, or scalene.
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Example 5 Finding Missing Values
ALGEBRA Find the measures of the sides of isosceles triangle KLM with base KL.
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Triangle Angle Relationships
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Example 1
Find the measure of 1, 2, And 3.
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Exterior Angles of a Triangle
• An Exterior Angle of a triangle is an angle that
forms a linear pair with an interior angle (or angle
of) a triangle.
• Remote Interior Angles are angles that are not
adjacent to the exterior angle.
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Examples
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Exterior Angles of a Triangle
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Corollaries
• Corollary – A theorem with a proof that follows as a
direct result of another theorem. These two follow
directly from the Triangle Angle-Sum Theorem.
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Examples
Find the measure of each numbered
angle.
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Examples
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Classwork: Text p. 241, 21-26, 30-35;
p. 251, 17-20; 24-29
Homework: HW Due 10 29, part 1, 1-10
part 2, 3-11