6-1: Congruent Figures, Classifying Triangles, and Related Theorems

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Presentation transcript:

6-1: Congruent Figures, Classifying Triangles, and Related Theorems Unit 6 English Casbarro

Classifying Triangles Triangles can be classified in two different ways: 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°) 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. b. c. 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. What is the sum of the measures of the interior angles of polygon ABCDEFG? b.

Homework Assignment 4-2 Skills Practice: 9-15 4-2 Practice: 6-11, 14