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Geometry Day 26

Geometry Day 26. Today’s Agenda. Classify triangles according to their sides and/or angles Investigate and prove certain theorems about triangles. Interior Angle Sum Theorem Exterior Angle Theorem. Notation.

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Geometry Day 26

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  1. Geometry Day 26

  2. Today’s Agenda • Classify triangles according to their sides and/or angles • Investigate and prove certain theorems about triangles. • Interior Angle Sum Theorem • Exterior Angle Theorem

  3. Notation • Triangles are noted with the symbol , and are named after their three vertices (in any order). • Ex: ABC, ACB, BAC, BCA, CAB, CBA all refer to this triangle. A C B

  4. Triangle Classifications • We have previously categorized triangles according to the types of angles they have. • Acute • Obtuse • Right • Equiangular • We can also categorize them according to their sides. • A scalene triangle has no sides that are the same length. • An isosceles triangle has at least two sides that are the same length. • An equilateral triangle has all three sides the same length. • An equilateral triangle is a special kind of isosceles triangle.

  5. Classifying Triangles • Lesson 4-1 is largely review. Tonight, read over 4-1, including the examples, and make sure you are familiar with that material.

  6. Triangles – Interior Angles • A triangle has three interior angles, which are the angles formed by the sides.

  7. Exterior Angles • The exterior angle of a polygon is the angle formed by extending one of its sides.

  8. Turn to p. 243 • Complete the activities on p. 243 in your textbook. • Use your straight-edge to draw three different triangles – acute, right, and obtuse – and cut them out. • The first activity involves the interior angles of a triangle. Perform the given instructions for each triangle, then answer the questions. Form a conjecture about the interior angles of any triangle. • The second activity involves the exterior angle of a triangle. Perform the instructions on each of your three triangles, then answer those questions. Form a conjecture about the exterior angle of a triangle.

  9. Proofs • We are now going to prove our conjectures. • Given: ABCProve: mA + mB + mC = 180 B A C

  10. Triangle Interior Angle Sum Theorem • This proof requires use of an auxiliary line, which is a line or segment we add (usually dotted) to help us examine geometric relationships. • Like any step, we must be able to justify the line we draw. B A C

  11. Triangle Interior Angle Sum Theorem • Given a line and a point, we can construct exactly one line parallel to the line that passes through the point. B D A C

  12. Triangle Interior Angle Sum Theorem • We’ll number the angles for convenience. • Can you use the diagram to finish the proof? Discuss. B D 4 5 3 2 1 A C

  13. Exterior Angle Theorem • Now try this. • Given: ABCProve: m4 = m1 + m2 2 1 4 3

  14. Homework 15 • Read 4-1 • Workbook, pp. 44, 46

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