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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.

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Quadrilaterals how do we solve them

QUADRILATERALS: HOW DO WE SOLVE THEM?

By: Steve Kravitsky

&

Konstantin Malyshkin


Aim how do we solve proofs of quadrilaterals
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 quadrilaterals1
AIM: HOW DO WE SOLVE PROOFS OF QUADRILATERALS?

Quadrilaterals

Parallelogram

Trapezoid

Rectangle

Rhombus

Isosceles Trapezoid

Square


Aim how do we solve proofs of quadrilaterals2
AIM: HOW DO WE SOLVE PROOFS OF QUADRILATERALS?

Properties of a Square:

1. All rectangle properties

2. All rhombus properties

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


Aim how do we solve proofs of quadrilaterals3
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 quadrilaterals4
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 quadrilaterals5
AIM: HOW DO WE SOLVE PROOFS OF QUADRILATERALS?

~

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 quadrilaterals6
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


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