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Warm UP

Warm UP. 1. Find the sum of the measures of the interior angles of the convex polygon. 1 . 19-gon. 2. The measure of an interior angle of a regular polygon is given. Find the number of sides in each polygon. 2 . 140. 3. Solve for x. x. 47. Section 8.2 Properties of Parallelograms.

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Warm UP

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  1. Warm UP 1. Find the sum of the measures of the interior angles of the convex polygon. 1. 19-gon 2. The measure of an interior angle of a regular polygon is given. Find the number of sides in each polygon. 2. 140 3. Solve for x. x 47

  2. Section 8.2 Properties of Parallelograms

  3. What is a Parallelogram? A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

  4. What makes a parallelogram special? Lets explore its properties…

  5. Parallelogram Exploration • Mark a point somewhere along the bottom edge of your index card. • Connect that point to the top right corner of the index card to form a triangle.

  6. Parallelogram Exploration • Cut along the line to remove the triangle. • Attach the triangle to the left side of the rectangle. • What shape have you created? Parallelogram

  7. Parallelogram Exploration • Measure the lengths of the sides of your parallelogram. • Measure the angles of your parallelogram. • Add together your consecutive angles. What do you notice? Parallelogram

  8. Theorem 8.3: If a quadrilateral is a parallelogram, then its opposite sides are congruent. Q R Theorem 8.4: If a quadrilateral is a parallelogram, then its opposite angles are congruent. P S

  9. Theorem 8.5: If a quadrilateral is a parallelogram, then its consecutive angles are supplementary. Q R Why its true… P S

  10. Parallelogram Exploration • Draw both of the diagonals of your parallelogram. • Measure the distance from each corner to the point where the diagonals intersect (point M). M What do you notice?

  11. Theorem 8.6: If a quadrilateral is a parallelogram, then its diagonals bisect each other. Q R M P S

  12. On the back of your parallelogram write the following Properties of a Parallelogram Both pairs of opposite sides are parallel Opposite sides are congruent Opposite angles are congruent Consecutive angles are supplementary Diagonals bisect each other

  13. Homework*Handout*

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