quadrilaterals: how do we solve them?
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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. - PowerPoint PPT PresentationTRANSCRIPT
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?
Quadrilaterals
Parallelogram
Trapezoid
Rectangle
Rhombus
Square
Isosceles Trapezoid
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:1. All six parallelogram properties
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 properties2. 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:1. Exactly one pair of parallel sides
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
M
H T
A
Q
~
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
Congruent parts of congruent triangles are congruent
If alternate interior angles are congruent when lines are cut buy a transversal are congruent
Vertical angles are congruent
ASA = ASA
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 1-5Page 232, questions 1-5Page 222, questions 17 and 20