6-1: Congruent Figures, Classifying Triangles, and Related TheoremsUnit 6
Classifying TrianglesTriangles can be classified in two different ways:
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°)
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 TheoremThe 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 problems1. Find the angle measures. a.
d.2. One of the steps in making an origami crane
involves folding a square sheet of paper into
the shape shown.
b. Use the Triangle Sum Theorem
to find 3.What is the sum of the measures of the
interior angles of polygon ABCDEFG?