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Triangle Patterns and Polygon Conjectures

Explore angle relationships in triangles and polygons, make conjectures, and discover polygon theorems. Find trends and draw conclusions based on geometric patterns. Learn about regular and irregular polygons.

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Triangle Patterns and Polygon Conjectures

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  1. Polygon Information

  2. Triangle Information Consider this pattern: 30+60+90=180 45+45+90=180 40+50+90=180 10+80+90=180 Based on this, what can you say about the acute angles in a right triangle?

  3. Try it! • Make a conjecture about the angles in an equiangular triangle.

  4. Triangle Theorem • If 2 angles of one triangle are congruent to 2 angles of another triangle, then make a conjecture about the 3rd angle.

  5. Congruent Polygons

  6. Polygon Vocabulary

  7. Not Regular Polygons Regular Polygons Make a conjecture about regular polygons

  8. Convex Concave

  9. Polygon Theorems

  10. FIND THE TREND!

  11. Examples • In ABC, and . Find the . • Based on the figure, write a conjecture about ADB and CBD.

  12. Examples • Write a conjecture given the figure below. R is the midpoint of .

  13. Examples • Given that the interior angles and exterior angles of a regular polygon are congruent, what is the name of the polygon.

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