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Geometry

9. Geometry. Ancient and Modern Mathematics Embrace. 9.2. Polygons. Understand the basic terminology and properties of polygons. Solve problems involving angle relationships of polygons . Use similar polygons to solve problems.

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Geometry

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  1. 9 Geometry Ancient and Modern Mathematics Embrace

  2. 9.2 Polygons • Understand the basic terminology and properties of polygons. • Solve problems involving angle relationships of polygons. • Use similar polygons to solve problems. • Be aware of some differences between Euclidean and non-Euclidean geometries.

  3. Polygons

  4. Polygons

  5. Polygons and Angles • Example: Find the sum of the measures of the interior angles in ΔABC. • Solution: Construct line mcontaining line segment AC and a second line l through point B parallel to m. (continued on next slide)

  6. Polygons and Angles m1 = m 4 (alternate interior angles) m 3 = m 5 (alternate interior angles) m 1 + m 2 + m 3 = m 4 + m 2 + m 5 = 180°

  7. Find the measure of angles in a triangle m<B = m<A, m<C = 5 + 3m<A Use the information above to find the angles of triangle ABC.

  8. Find the measure of angles in a triangle m<B = m<A, m<C = 5 + 3m<A Use the information above to find the angles of triangle ABC. Solution: x + x + (5+ 3x) = 180 5x + 5 = 180 x = 35 <A =35 <B =35 <C= 110

  9. Polygons and Angles

  10. Polygons and Angles • Example: A billboard is to be in the shape of a giant star. Determine the angle measure of each point of the star. (continued on next slide)

  11. Polygons and Angles • Solution: • Pentagon angles: A straight angle equals 180°, EZV and EVZ each have measure 72°. E has measure 180° – 72° – 72° = 36°. (continued on next slide)

  12. Polygons

  13. Similar Polygons

  14. Similar Polygons • Example: A bridge is to be used to cross a river. The distances in the two right triangles were measured. Use this information to find the distance, d, across the river. (continued on next slide)

  15. Similar Polygons • Solution: mBAC = mDAE (vertical angles) mC = mD = 90° (right angles) ΔACB is similar to ΔADE

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