Geometry-07-Quadrilaterals-and-Other-Polygons PDF

QUADRILATERALS AND OTHER POLYGONS 7.1 ANGLES OF POLYGONS After this lesson… I can find the sum of the interior angle measures of a polygon. I can find interior angle measures of polygons. I can find exterior angle measures of polygons. 7.1 ANGLE...

QUADRILATERALS AND OTHER POLYGONS 7.1 ANGLES OF POLYGONS After this lesson… I can find the sum of the interior angle measures of a polygon. I can find interior angle measures of polygons. I can find exterior angle measures of polygons. 7.1 ANGLES OF POLYGONS  Polygon  Closed figure made of straight segments  Diagonal  Segment that joins nonconsecutive vertices 7.1 ANGLES OF POLYGONS  All polygons can be separated into triangles  The sum of the angles of a triangle is 180°  For the pentagon, multiply that by 3 Polygon Interior Angles Theorem Sum of the measures of the interior angles of a n- gon is Sum of the measures of the interior angles of a quadrilateral is 360° 7.1 ANGLES OF POLYGONS  Equilateral Polygon  All sides congruent  Equiangular Polygon  All angles congruent  Regular Polygon  All sides and angles congruent 7.1 ANGLES OF POLYGONS Polygon Exterior Angles Theorem Sum of the measures of the exterior angles of a convex polygon 360°  What is the measure of an exterior angle of a regular pentagon?  What is the measure of an interior angle of a regular pentagon?  7.2 PROPERTIES OF PARALLELOGRAMS After this lesson… I can prove properties of parallelograms. I can use properties of parallelograms. I can solve problems involving parallelograms in the coordinate plane. 7.2 PROPERTIES OF PARALLELOGRAMS  Definition of parallelogram  Quadrilateral with opposite sides parallel Opposite sides of parallelogram are congruent Opposite angles of a parallelogram are congruent 7.2 PROPERTIES OF PARALLELOGRAMS Consecutive angles in a parallelogram are supplementary  Remember from parallel lines that consecutive interior angles are supplementary Diagonals of a parallelogram bisect each other  Draw diagonals on your parallelogram  Measure each part of the diagonals to see if they bisect each other. 7.3 PROVING THAT A QUADRILATERAL IS A PARALLELOGRAM  For what values of x and y is quadrilateral STUV a parallelogram? 7.3 PROVING THAT A QUADRILATERAL IS A PARALLELOGRAM  Find x so that MNPQ is a parallelogram.  Try #14  7.4 PROPERTIES OF SPECIAL PARALLELOGRAMS After this lesson… I can identify special quadrilaterals. I can explain how special parallelograms are related. I can find missing measures of special parallelograms. I can identify special parallelograms in a coordinate plane. 7.4 PROPERTIES OF SPECIAL PARALLELOGRAMS  All of these are parallelograms  Rhombus  Four ≅ sides  Rectangle  Four right s  Square  Rhombus and Rectangle  Four ≅ sides  Four right s 7.4 PROPERTIES OF SPECIAL PARALLELOGRAMS 7.4 PROPERTIES OF SPECIAL PARALLELOGRAMS  For any rectangle EFGH, is it always or sometimes true that ?  Classify the figure.  Try #2, 8 7.4 PROPERTIES OF SPECIAL PARALLELOGRAMS  Diagonals Rhombus: diagonals are perpendicular Rhombus: diagonals bisect opposite angles Rectangle: diagonals are congruent  7.5 PROPERTIES OF TRAPEZOIDS AND KITES After this lesson… I can identify trapezoids and kites. I can use properties of trapezoids and kites to solve problems. I can find the length of the midsegment of a trapezoid. I can explain the hierarchy of quadrilaterals. 7.5 PROPERTIES OF TRAPEZOIDS AND KITES  Trapezoid  Quadrilateral with exactly one pair of parallel sides  If the legs are ≅, then the trap is isosceles 7.5 PROPERTIES OF TRAPEZOIDS AND KITES If isosceles trapezoid, then each pair of base angles is ≅. If isosceles trapezoid, then diagonals are ≅.  The converses are also true 7.5 PROPERTIES OF TRAPEZOIDS AND KITES  Show that ABCD is a trapezoid. Then decide whether it is isosceles.  Try #2 7.5 PROPERTIES OF TRAPEZOIDS AND KITES  Midsegment of a Trapezoid  Segment connecting the midpoints of each leg Midsegment Theorem for Trapezoids The midsegment of a trapezoid is parallel to the bases and its length is the average of the lengths of the bases. 7.5 PROPERTIES OF TRAPEZOIDS AND KITES  Kites  Quadrilateral with 2 pairs of consecutive congruent sides If kite, then the diagonals are perpendicular. If kite, then exactly one pair of opposite angles are congruent. 7.5 PROPERTIES OF TRAPEZOIDS AND KITES 7.5 PROPERTIES OF TRAPEZOIDS AND KITES  Give the most specific name for the quadrilateral.  Try #22 ACTIVITY  1) Draw as many different quadrilaterals that you can with the following properties  a) congruent diagonals.  b) perpendicular diagonals  c) exactly one pair of congruent sides  d) at least one pair of opposite angles congruent  e) at most one pair of opposite congruent sides