UNIT 2

QUADRILATE

RALS

SECTION 1

TYPE

S OF

ANGLES

NAME THE CONGRUENT ANGLES!• 1, 4, 5, 7

• 2, 3, 6, 8

DIFFERENT TYPES OF ANGLES• Vertical angles: 1 and 4, directly

across from each other; always congruent

• Alternate interior angles: 3 and 6, inside the parallel lines on opposite sides of the transversal (form a “Z”)• Congruent when lines are parallel

• Corresponding angles: 1 and 5. in the same place at each intersection

• Consecutive angles: 3 and 5, inside the parallel lines on the same side• Supplementary when lines are parallel

• Supplementary = add up to 180°• Angles that form a line are also

supplementary, ( 1 and 2)

FIND THE OTHER ANGLE MEASURES.

=120°

ANGLES OF A POLYGON

• Interior angles of a polygon add up to 180(n – 2)• n is the number of sides

• Exterior angles of a polygon ALWAYS add up to 360°

Type of Polygon

nSum of Interior Angles

Measure of One Interior Angle

Sum of Exterior Angles

Measure of One

Exterior Angle

Triangle

Quadrilateral

3 180° 360°

4 360° 360°

REGULAR POLYGONS• Regular polygon: polygon where all sides and angles are

congruent

• How do we find the measure of ONE angle on a regular polygon?• Divide the sum by the number of sides

• Interior angle:

• Exterior angle:

nn )2(180

n360

Type of Polygon

nSum of Interior Angles

Measure of One Interior Angle

Sum of Exterior Angles

Measure of One

Exterior Angle

Triangle 3 180° 360°60° 120°

WRAP UP

• Exit Slip

• Unit 2 Homework Packet Due Friday

• Unit 2 Test Friday

SECTION 2

PARALL

ELOGRAMS &

RHOMBUSES

WHAT IS THIS CALLED?

PARALLELOGRAM!

PROPERTIES OF A PARALLELOGRAM

• Opposite sides are parallel and congruent• •

• Opposite angles are congruent•

• Diagonals bisect each other• Bisect = to split in

half

CBADCDAB ,

CBADCDAB ,

CDAABCBCDDAB ,

EXAMPLE 1

In the accompanying diagram of parallelogram ABCD, diagonals AC and BD intersect at E, AE = 2x + 8, and EC = 4x – 22. What is the value of x?

• What do AE and EC form?

• What do we know about the diagonals of a parallelogram?

• What do we now know about AE and EC?

• BONUS: Can you find the pairs of alternate interior angles and consecutive angles?

EXAMPLE 2

In the accompanying diagram of parallelogram ABCD, diagonals AC and BD intersect at E, BE = ½x and ED = x – 4. What is the value of x?

WRAP-UP

• Exit Slip

• Unit 2 Homework Packet

• Unit 2 Test

SECTION 3

RECTANGLE

S, SQUARES, T

RAPEZOID

S

SPECIAL QUADRILATERALS

Rhombus

Rectangle

SquareParallelogram

Quadrilateral

Trapezoid

RHOMBUS

• A parallelogram with all four sides congruent

• Has all the properties of a parallelogram, plus:• 4 congruent sides• Diagonals are

perpendicular

• Food for thought ： Are all rhombuses parallelograms? Are all parallelograms rhombuses?

EXAMPLE 1

PQRS is a rhombus. PQ = 2/3x and SP = 2x – 12. Find x.

(Hint: Draw a sketch! You should always label the points of any figure in order.)

RECTANGLE

• Parallelogram with four right angles

• Has all the properties of a parallelogram, plus:• Four right angles• Congruent diagonals

• Are all rectangles parallelograms? Are all parallelograms rectangles?

EXAMPLE 2

Rectangle ABCD has angle ADB = 4x – 25 and angle DBC = x + 35. Find the measure of angle BDC.

SQUARE

• Parallelogram with four congruent sides and four right angles

• Diagonals are congruent and perpendicular

• Combination of a rhombus and a rectangle

EXAMPLE 3

TRAPEZOID

• Quadrilateral with only ONE pair of opposite sides parallel

• Isosceles trapezoid• Legs (non-parallel sides)

are congruent• Base angles are

congruent• Diagonals are congruent

EXAMPLE 4

COMPARING QUADRILATERALS

ShapeFour Sides

Opposite Sides

Parallel

All Sides Congrue

nt

Four Right

Angles

Congruent

Diagonals

Perpendicular Diagonals

Quadrilateral

   

Parallelogram

   

Rhombus    

Rectangle    

Square    

Identify which shapes possess each property:

WRAP UP

• Exit Slip

• Unit 2 Test Monday

• Unit 2 Homework Packet Due Monday