Download Quadrilateral Sum Conjecture Pentagon Sum Conjecture Polygon

Name ________________________ Objectives: •
Discover the sum of the angle measures in a polygon. •
Practice construction skills •
Develop reasoning, problem‐solving skills, and cooperative behavior Quadrilateral Sum Conjecture The sum of the measures of the four interior Pentagon Sum Conjecture The sum of the measures of the five interior angles of any quadrilateral is ____________. angle of any pentagon is _____________. Polygon Sum The sum of the measures of the n interior Conjecture angles of an n‐gon is _______. (If a polygon has n sides, it is called an __________.) EXAMPLE: The sum of the measures of the interior angles of a regular polygon is 2340°. How many sides does the polygon have? Objectives •
Discover the sum of the measures of the exterior angles of a polygon •
Write formulas for the measure of the interior angle of an equiangular polygon •
Practice construction skills •
Develop reasoning, problem‐solving skills, and cooperative behavior Exterior Angle Sum Conjecture For any polygon, the sum of the measures of a set of exterior angles is ___________. If these are equiangular polygons, how do we find the measure of just one interior angle when we know the sum of the interior angles? Equiangular Polygon Conjecture The measure of each interior angle of an equiangular n‐gon is _____________ or _______________ Using the Exterior Angle Sum Conjecture, write the formula for the measure of each exterior angle in an equiangular polygon. Exterior angle in an equiangular polygon Each exterior angle in an equiangular polygon is: _____________. EX. A. How many sides does a regular Polygon have if each exterior angle measures 30°? Objectives • Discover properties of kites and trapezoids • Learn new vocabulary • Practice construction skills Kite A quadrilateral with exactly _____ distinct pair of congruent consecutive sides. Kite angle conjecture The _____________ angles of a kite are __________. Kite Diagonals conjecture The diagonals of a kite are _________________. Kite Diagonal Bisector Conjecture The diagonal connecting the vertex angles of a kite is the _______________ of the other diagonal. Kite Angle Bisector Conjecture The ______________ angles of a kite are __________ by a ____________. Trapezoid A quadrilateral with exactly ______ pair of parallel sides. Trapezoid Consecutive Angles Conjecture The consecutive angles
between the bases of a trapezoid are ____________________.
Isosceles Trapezoid Conjecture The base angles of an isosceles trapezoid are _______________. Isosceles Trapezoid Diagonals Conjecture The diagonals of an isosceles trapezoid are ____________. Three midsegments conjecture The three midsegments of a triangle divide it into ______________________________ Triangle A midsegment of a triangle is midsegment _______ to the conjecture third side and ______ the length of __________ Trapezoid The midsegment of a trapezoid is midsegment ____________ to the bases and is conjecture equal in length to ____________________________