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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
Triangles and Classification
• Triangle – A three sided polygon.
• Classifying Triangles
By Angle
By Sides
Classifying by Angles
Examples
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.
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.
A. acute
B. equiangular
C. obtuse
D. right
Classify ΔACD as acute, equiangular, obtuse, or right.
Classifying by Sides
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.
A. equilateral
B. isosceles
C. scalene
If point C is the midpoint of BD, classify ΔABC as equilateral, isosceles, or scalene.
Example 5 Finding Missing Values
ALGEBRA Find the measures of the sides of isosceles triangle KLM with base KL.
Triangle Angle Relationships
Example 1
Find the measure of 1, 2, And 3.
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.
Examples
Exterior Angles of a Triangle
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.
Examples
Find the measure of each numbered
angle.
Examples
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
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