1. INTERIOR ANGLES THEOREM FOR QUADRILATERALS By: Katerina Palacios 10-1 T2 Geometry

2. The interior angles theorem for quadrilaterals says that sum of the angle measures of a triangle has to equal the sum of the angle measures The formula for this is n-2 (180) n equals the number of sides. 2 4 33-2=1(180) =180 degrees 56 7 8 4-2=2(180) =360 degrees 1 23 45 6 6-2=4(180) =720 deegres

3. There are 4 theorems of parallelograms: Theorem 6-3-1 states that if one pair of opposite sides of a quadrilateral is congruent and parallel then the quadrilateral is also a parallelogram. Converse: If a quadrilateral is also a parallelogram then one pair of opposite sides are congruent and also parallel. A B C D AB is congruent to CD So AC is congruent to BD

4. Theorem 6-3-2 If the two pairs of opposite sides are congruent then the quadrilateral is also a parallelogram. Converse: If a quadrilateral is also a parallelogram then the the 2 pairs of opposite sides are congruent Theorem 6-3-3 If the two pairs of opposite angles are congruent then the quadrilateral is also a parallelogram Converse: If a quadrilateral is also a parallelogram then the two pairs of opposite angles are congruent. A BC D <A is congruent to <C <B is congruent to <D

5. To prove a quadrilateral is also a parallelogram you have to use the properties and the theorems to determine that. First of all if an quadrilateral has two pair of opposite sides and opposite angles that are congruent than it is also a parallelogram. Since this is one theorem of a parallelogram. Also you know when it is a parallelogram. When diagonals bisect each other. So you have to understand what a parallelogram is in order to know if the quadrilateral is also a parallelogram or not. Diagonals bisect each other D E F G <D is congruent to <F <G is congruent to <E A BC D AD is congruent to BC AB is congruent to CD