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Classifying and Analyzing Triangle Angle Relationships

This comprehensive guide explores various methods for classifying triangles based on their angles and sides. Learn how to identify acute, obtuse, and right triangles, and understand the properties associated with each type. Discover the Triangle Sum Theorem, which states that the interior angles of a triangle sum up to 180 degrees, and the Exterior Angle Theorem, which relates an exterior angle to the interior angles. Additionally, apply these principles to solve problems involving real-world contexts, such as designing a coat hanger with specific dimensions and angles.

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Classifying and Analyzing Triangle Angle Relationships

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  1. 4-1 and 4-2 Classifying Triangles Angle Relationships in Triangles

  2. Classify Triangles By Angles

  3. Classify Triangles By Sides

  4. Classify each triangle by angles and sides 6 A 8 11 10 • ∆ NSE • ∆ ANE • ∆ AEK • ∆ ASK • ∆ AES N 115◦ 12 5.1 25◦ 40◦ 70◦ S E K

  5. Find the value of x, y and ∆ side lengths 6) 7) 10x – 4 6y 13 – 2x x2 – 5x – 15 4y + 12 2 – 4x

  6. 8) You are bending a wire to make a coat hanger. The length of the wire is 65 cm. You need 25 cm to make the hook of the hanger. The triangular portion of the hanger is an isosceles triangle. The length of one leg of this triangle is half the length of the base. a) Sketch the hanger. b) Give the dimensions of the triangular portion.

  7. Triangle Sum Theorem • The sum of the angles measures of a triangle is ____________________.Corollaries of the Thm • Acute angles in a right triangle are complementary. • Measure of each angle in an equiangular triangle is 60◦.

  8. Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote (nonadjacent) interior angles. 2 4 1 3

  9. Third Angles Theorem If two angles of one triangle are congruent to two angles of another triangle, then the third angles are ____________. 50◦ 50◦ 70◦ 70◦

  10. Ex: Apply the new theorems to solve 10) In ∆SMD, m<S=55 and m<M is four times larger than m<D. Find m<M and m<D. 9)

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