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Transcript
SCRIPT: By Christa Walters Safety symbol: all Copyrights to CW productions. Don’t be afraid. It won’t kill you, only make you stronger…. A closed figure that is formed by 3 or more segments. 1. Side: one of the segments that is part of the polygon, which joins the vertices. 2. Diagonal: segment that connects any two nonconsecutive vertices. 3. Vertex: the common endpoint between two segments. (Rosie standing by the chair) says: Jonathan responds by telling her more information: (eloquent, teacher-like, and demanding) Convex • A polygon in which on or other vertices are pointing in. • A polygon in which the vertices are pointing concave out. A POLYGON IN WHICH ALL SIDES ARE CONGRUENT. A POLYGON IN WHICH ALL ANGLES ARE CONGRUENT. The sum of the interior angle measurement of a polygon with n sides is (n-2)180 (Joe slowly enters the room and joins the conversation.) EX 1. of an octagon: (8-2)180 = 1080/8= the m. of 1 angle= 135 degrees 2. Of a nonagon: (9-2)180= 1260/9= m. of 1 angle= 140 degrees 3. Of a pentagon: (10-2)180= 1440/10= m. of 1 angle= 144 degrees (Rosie nods her head and continues to ask questions) A quadrilateral with two pairs of parallel sides.Use the symbol ▭ to name a parallelogram. ( already night time and Rosie still confused, has a dream about…………) THEOREM 6-2-1 1. If a quadrilateral is a parallelogram,then its opposite sides are congruent (▭ ---- opp. Sides are congruent) (if opposite sides are congruent ---- it´s a▭) B C A D AB congruent to CD BC congruent to DA THOREM 6-2-2 2. If a quadrilateral is a parallelogram,then uts opposite angles are congruent. (▭---- opp. Angles are congruent)(if opposite angles are congruent,then it´s a ▭) THOEREM 6-2-3 3. If a quadrilateral is a parallelogram, then its consecutive angles are supplementary. (▭----- cons..angles are supp)(if con.angles are supp.---then it is a ▭) THEOREM 6-2-4 4. If a quadrilateral is a parallelogram, then its diagonals bisect each other, (▭----diagnals bisect each other) (if diagonals bisect each other---- it´s a ▭) Opposite sides are parallel Opposite sides are congruent Consecutive angles are supplementary Diagonals bisect each other Opposite angles ate congruent One set of congruent and parallel sides. QUADRILATERAL PARALLELOGRAM RECTANGLE RHOMBUS SQUARE A quadrilateral with exactly one pair of parallel sides, each of the parallel sides is called a base and the nonparallel sides are called legs. IF A TRAPEZOID IS ISOSCELES…. WHAT SHOULD ROSIE KNOW? If a quadrilateral is an isosceles trapezoid, then each pair of base angles are congruent. If a trapezoid has one pair of congruent base angles,then the trapezoid is isosceles. A trapezoid is isosceles if and only if the diagonals are congruent. The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases. midsegment mi It’s a quadrilateral with exactly two pairs of congruent consecutive sides. THEOREMS: If a quadrilateral is a kite, then its diagonals are perpendicular. If a quadrilateral is a kite,then exactly one pair of opposite angles are congruent.