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6.1 Polygons

Explore the concepts of polygons and their properties, including definitions of polygons and diagonals. Learn about the classifications and properties of quadrilaterals, focusing on the Quadrilateral Interior Angles Theorem where the sum of the angles is 360°. Discover the specific characteristics of parallelograms, such as congruent opposite sides and angles, supplementary consecutive angles, and the property that diagonals bisect each other. Engage with examples and practice problems to enhance your understanding and application of these geometric concepts.

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6.1 Polygons

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  1. 6.1 Polygons

  2. Vocabulary • Polygon: plane figure formed by three or more segments (called sides). • Diagonal: segment that joins 2 non-consecutive vertices

  3. Classifying Polynomials

  4. Example 1 • Is the figure a polygon? Explain your reasoning.

  5. Quadrilaterals • Quadrilateral Interior Angles Theorem • The sum of the measures of the interior angles of a quadrilateral is 360°

  6. Example 2 • Find the measure of the missing angle within each quadrilateral.

  7. 6.2 Properties of Parallelograms • Parallelogram: quadrilateral with BOTH pairs of opposite sides parallel

  8. Theorems about Parallelograms • If a quadrilateral is a parallelogram, then its opposite sides are congruent. • If a quadrilateral is a parallelogram, then its opposite angles are congruent. • If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

  9. Example 1 • FGHJ is a parallelogram. Find JH and FJ.

  10. Example 2 • PQRS is a parallelogram. Find the missing angle measures.

  11. You Try It… • Find the missing side lengths or angle measures as indicated.

  12. One more theorem… • If a quadrilateral is a parallelogram, then its diagonals bisect each other. • REMEMBER: to BISECT a segment means to divide the segment into two congruent segments.

  13. Example 3 • TUVW is a parallelogram. Find TX.

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