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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 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?
Try it! • Make a conjecture about the angles in an equiangular triangle.
Triangle Theorem • If 2 angles of one triangle are congruent to 2 angles of another triangle, then make a conjecture about the 3rd angle.
Not Regular Polygons Regular Polygons Make a conjecture about regular polygons
Convex Concave
Examples • In ABC, and . Find the . • Based on the figure, write a conjecture about ADB and CBD.
Examples • Write a conjecture given the figure below. R is the midpoint of .
Examples • Given that the interior angles and exterior angles of a regular polygon are congruent, what is the name of the polygon.