1. QUADRILATERALS: HOW DO WE SOLVE THEM?
By: Steve Kravitsky
&
Konstantin Malyshkin

2. AIM: HOW DO WE SOLVE PROOFS OF QUADRILATERALS?
Homework: Textbook Page – 261, Questions 1-5 Do Now: What are the two groups that quadrilaterals break off into? Quadrilaterals
Parallelogram
Trapezoid

3. AIM: HOW DO WE SOLVE PROOFS OF QUADRILATERALS?
Parallelogram
Trapezoid
Rectangle
Rhombus
Isosceles Trapezoid
Square

4. AIM: HOW DO WE SOLVE PROOFS OF QUADRILATERALS?
Properties of a Parallelogram:
1. Both pairs of opposite sides are parallel
2. Both pairs of opposite sides are congruent
3. Both pairs of opposite angles are congruent
4. Consecutive angles are congruent
5. A diagonal divides it into two congruent triangles
6. The diagonals bisect each other.
Properties of a Rectangle:
1. All six parallelogram properties
2. All angles are right angles
3. The diagonals bisect each others
Properties of a Rhombus:
2. All four sides are congruent
3. The diagonals bisect the angles
4. The diagonals are perpendicular to each other
Properties of a Square:
1. All rectangle properties
2. All rhombus properties

5. AIM: HOW DO WE SOLVE PROOFS OF QUADRILATERALS?
Properties of a Trapezoid:
1. Exactly one pair of parallel sides
Properties of a Isosceles Trapezoid:
2. Non-parallel sides are congruent
3. The diagonals are congruent
4. The base angles are congruent

6. AIM: HOW DO WE SOLVE PROOFS OF QUADRILATERALS?~
Given: Quadrilateral MATH, AH bisects MT at Q, TMA = MTH Prove: MATH is a parallelogram H T Q M A

7. AIM: HOW DO WE SOLVE PROOFS OF QUADRILATERALS?
Statement
Reason
AH Bisects MT at Q
Given
TMA = MTH
MA HT
MQA = HQT
MQA = TQH
MA = HT
MATH is a parrallelogram ~
MQ = QT
A bisector forms two equal line segments ~
Given
If alternate interior angles are congruent when lines are cut buy a transversal are congruent ~
Vertical angles are congruent  ~
ASA = ASA ~ ~
Congruent parts of congruent triangles are congruent
If one pair of opposite sides of a quadrilateral is both parallel and congruent, he quadrilateral is a parallelogram.

8. AIM: HOW DO WE SOLVE PROOFS OF QUADRILATERALS?
Pair Share:
Workbook Pages : Page 245, questions 1-5
Page 232, questions 1-5
Page 222, questions 17 and 20