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Classifying Triangles by Sides and Angles - Geometry Tutorial

Learn how to classify triangles by sides and angles in this comprehensive geometry tutorial. Understand triangles, their properties, and how to determine if they are right, acute, or obtuse. Practice examples and coordinate plane analysis included.

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Classifying Triangles by Sides and Angles - Geometry Tutorial

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  1. 4.1 – Classifying Triangles

  2. Triangles • A polygon with three sides. • The corners are called vertices • A triangle with vertices A, B, and C is called “triangle ABC” or “

  3. Classifying Triangles by Sides

  4. Classifying Triangles by Angles

  5. Example 1:Classify triangles by sides and angles a) b) c) 7 40° 15° 25 24 70° 70° 120° 45° • Solutions: • Scalene, Right • Isosceles, Acute • Scalene, Obtuse

  6. Example 2:Classify triangles by sides and angles Now you try… a) b) c) 5 110° 3 5 5 4 5

  7. Review: The distance formula To find the distance between two points in the coordinate plane…

  8. Classify PQOby its sides. Then determine if the triangle is a right triangle. Use the distance formula to find the side lengths. STEP1 2 2 – – ( ( ) ) OP = + + 2 2 – – ( ( ) ) y x x y y y x x 2 1 2 2 2 1 1 1 2 2 ( – ( ) (– 1 ) ) 0 2 – 0 2.2 + = = 5 OQ = 2 2 ( – ( ) 6 ) 0 – 0 3 6.7 + = = 45 EXAMPLE 3 Classify a triangle in a coordinate plane SOLUTION

  9. PQ = 2 2 ( – ) 6 (– 1 ) ) 3 – ( 2 7.1 + = = Check for right angles by checking the slopes. There is a right angle in the triangle if any of the slopes are perpendicular. STEP2 The slope ofOPis 2 – 0 3 – 0 1 . – 2. The slope ofOQis = = – 2 – 0 2 6 – 0 2 – ( ) + 2 – ( ) so OPOQand POQ is a right angle. y y x x 1 1 2 2 50 ANSWER Therefore, PQOis a right scalene triangle. EXAMPLE 3 Classify a triangle in a coordinate plane (continued)

  10. Example 4:Classify a triangle in the coordinate plane Now you try… Classify ΔABC by its sides. Then determine if the triangle is a right triangle. The vertices are A(0,0), B(3,3) and C(-3,3). Step 1: Plot the points in the coordinate plane.

  11. Example 4: (continued)Classify a triangle in the coordinate plane Step 2: Use the distance formula to find the side lengths: AB = BC = CA = Therefore, ΔABC is a ______________ triangle.

  12. Example 4: (continued)Classify a triangle in the coordinate plane Step 3: Check for right angles by checking the slopes. The slope of = The slope of = The slope of = Therefore, ΔABC is a ______________ triangle.

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