Transcript 6-1: Congruent Figures, Classifying Triangles, and Angle

6-1: Congruent Figures,
Classifying Triangles, and
Related Theorems
Unit 6
English Casbarro
Classifying Triangles
Triangles can be classified in two different ways:
1) By Angles
a) acute- all three angles are acute (less than 90°)
b) obtuse- one angle is obtuse (greater than 90°)
c) right- one angle is a right angle (equal to 90°)
2) By Sides
a) scalene- all sides have different lengths
b) isosceles- at least two sides are equal
c) equilateral- all three sides are equal
Angle Theorems- these theorems
are used in problems to find
measures of various angles.
 Angle-Sum Theorem: The sum of the angles of
a triangle is 180°.
 Exterior Angle Theorem: The measure of the
exterior angle of a triangle is equal to the sum
of the measures of the 2 remote interior
angles.
 Third Angle Theorem: If two angles of one
triangle are congruent to two angles of a
second triangle, then the third angles of the
triangles are congruent.
 Base Angle Theorem: If two sides of a triangle
are congruent, then the base angles opposite
the sides are congruent.
1. What are the measures of /1 and / 2?
Note: If any polygon is convex, then the sum of the measures of the
exterior angles is 360°.
Extension of Angle-Sum Theorem
 The sum of the measures of the
interior angles of an n-gon is:
180(n – 2)
Note: Each angle measures 900/7 ≈ 128.57
Turn in the following problems
1. Find the angle measures.
a.
c.
b.
d.
2. One of the steps in making an origami crane
involves folding a square sheet of paper into
the shape shown.
a.
b. Use the Triangle Sum Theorem
to find
3.
a. What is the sum of the measures of the
interior angles of polygon ABCDEFG?
b.
Homework Assignment
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4-2 Skills Practice: 9-15
4-2 Practice: 6-11, 14
4-5 Practice: 3, 5, 7, 8, 10-15, 20
6-1 Skills Practice: 4, 8-10, 11, 14