6.1 polygons

6.1 POLYGONS

VOCABULARYPolygon: plane figure formed by three or more segments (called sides).

Diagonal: segment that joins 2 non-consecutive vertices

CLASSIFYING POLYNOMIALSName # of Sides Sketch

Triangle

Quadrilateral

Pentagon

Hexagon

Heptagon

Octagon

Nonagon

Decagon

EXAMPLE 1Is the figure a polygon? Explain your reasoning.

QUADRILATERALS Quadrilateral Interior Angles Theorem

The sum of the measures of the interior angles of a quadrilateral is 360°

EXAMPLE 2Find the measure of the missing angle within each quadrilateral.

6.2 PROPERTIES OF PARALLELOGRAMS

Parallelogram: quadrilateral with BOTH pairs of opposite sides parallel

THEOREMS ABOUT PARALLELOGRAMS

1) If a quadrilateral is a parallelogram, then its opposite sides are congruent.

2) If a quadrilateral is a parallelogram, then its opposite angles are congruent.

3) If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

EXAMPLE 1FGHJ is a parallelogram. Find JH and FJ.

EXAMPLE 2PQRS is a parallelogram. Find the missing angle measures.

YOU TRY IT…Find the missing side lengths or angle measures as indicated.

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.

EXAMPLE 3TUVW is a parallelogram. Find TX.