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# QUADRILATERALS: HOW DO WE SOLVE THEM? - PowerPoint PPT Presentation

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?

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?

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 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 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

H

T

Q

M

A

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 QUADRILATERALS?

Pair Share:

Workbook Pages : Page 245, questions 1-5

Page 232, questions 1-5

Page 222, questions 17 and 20