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

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°)

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

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

  2. 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

  3. 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.

  4. 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°.

  5. 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

  6. 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.

  7. Homework Assignment • 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

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