QUADRILATERALS: HOW DO WE SOLVE THEM?

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Presentation transcript:

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

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

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

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

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

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

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.

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