GeometryGeometry

Today:• Class Attendance

/ Announcements• 6.4 Vocabulary

Review• Warm-Up• 6.4 Notes /

Practice• Begin Homework

Every moment in planning saves 3 or 4 in execution.

Crawford Greenwalt

1.

2.

3.

4.

5.

WARM-UPWARM-UP

What are the properties of a parallelogram?

6.3

6.4 – Rhombuses, 6.4 – Rhombuses, Rectangles, & SquaresRectangles, & Squares

Objectives:1.Know special parallelograms2.Know properties of special

parallelograms

Vocabulary:square, rhombus, rectangle

VocabularyVocabulary

Rectangle – a quadrilateral with 4 right angles

6.4

RECTANGLE FACTS:RECTANGLE FACTS:

Has all 5 properties of a parallelogram+ Has four right angles.+ Diagonals are congruent.

+ A parallelogram is a + A parallelogram is a rectangle iff the rectangle iff the diagonals are congruent.diagonals are congruent.

6.4

7 properties total7 properties total

VocabularyVocabulary

Rhombus – a quadrilateral with 4 congruent sides

6.4

RHOMBUS FACTS:RHOMBUS FACTS:

+ Diagonals are + Diagonals bisect angles.A parallelogram is a rhombus iff the A parallelogram is a rhombus iff the

diagonals are perpendicular.diagonals are perpendicular.

A parallelogram is a rhombus iff the A parallelogram is a rhombus iff the diagonals bisect the angles.diagonals bisect the angles.

6.4

Has all 5 properties of a parallelogram+ Has four congruent sides.

8 properties 8 properties totaltotal

VocabularyVocabulary

Square – a quadrilateral with 4 right angles and 4 congruent sides (both a rhombus and a rectangle)

6.4

SQUARE FACTSSQUARE FACTS

Has all 5 properties of a parallelogram

Has all properties of a rectangle (additional 2 properties).

6.4

10 properties total10 properties total

Has all properties of a rhombus (additional 3 properties).

Break TimeBreak Time

Take a few minutes to get up, stretch out, or try the following rebus puzzles.

To see redTo see red Travel Travel overseasoverseas

Quadrilaterals

(4 sides)

Parallelograms

(opp. sides ll)

Rhombus(all sides )

Rectangles(all right ’s)

Square(Rect & Rhomb)

6.6

• What type of quadrilateral is ABCD?

• Parallelogram• Rectangle

A B

CD

QUESTIONS ABOUT SPECIAL QUESTIONS ABOUT SPECIAL QUADRILATERALSQUADRILATERALS

Answer each question with A, S, N for always, sometimes, and never true.

1. A rectangle is a square

2. A square is a rhombus

3. A rectangle is a parallelogram

4. A rectangle is a rhombus6.4

Property ll rect

rhm

sqr kite

trp istrp

Both pairs of opposite sides parallel

Exactly 1 pair of opposite sides parallel

Diagonals perpendicular

Diagonals congruent

Diagonals bisect each other

Both pairs of opposite sides are congruent

Exactly one pair of opposite sides are congruent

All sides are congruent

Both pairs of opposite angles are congruent

Exactly one pair of opposite angles are congruent

All angles are congruent

Property ll rect

rhm

sqr kite

trp istrp

Both pairs of opposite.sides parallel XExactly 1 pair of opposite sides parallel

Diagonals perpendicular

Diagonals congruent

Diagonals bisect each other XBoth pairs of opposite sides are congruent XExactly one pair of opposite sides are congruent

All sides are congruent

Both pairs of opposite angles are congruent XExactly one pair of opposite angles are congruent

All angles are congruent

Property ll rect

rhm

sqr kite

trp istrp

Both pairs of opposite.sides parallel X XExactly 1 pair of opposite sides parallel

Diagonals perpendicular

Diagonals congruent XDiagonals bisect each other X XBoth pairs of opposite sides are congruent X XExactly one pair of opposite sides are congruent

All sides are congruent

Both pairs of opposite angles are congruent X XExactly one pair of opposite angles are congruent

All angles are congruent X

Property ll rect

rhm

sqr kite

trp istrp

Both pairs of opposite.sides parallel X X XExactly 1 pair of opposite sides parallel

Diagonals perpendicular XDiagonals congruent XDiagonals bisect each other X X XBoth pairs of opposite sides are congruent X X XExactly one pair of opposite sides are congruent

All sides are congruent XBoth pairs of opposite angles are congruent X X XExactly one pair of opposite angles are congruent

All angles are congruent X

Property ll rect

rhm

sqr kite

trp istrp

Both pairs of opposite.sides parallel X X X XExactly 1 pair of opposite sides parallel

Diagonals perpendicular X XDiagonals congruent X XDiagonals bisect each other X X X XBoth pairs of opposite sides are congruent X X X XExactly one pair of opposite sides are congruent

All sides are congruent X XBoth pairs of opposite angles are congruent X X X XExactly one pair of opposite angles are congruent

All angles are congruent X X

QUESTIONS ABOUT SPECIAL QUESTIONS ABOUT SPECIAL QUADRILATERALSQUADRILATERALS

List all the special quadrilaterals that have each property:

1. Diagonals are congruent

2. Diagonals are perpendicular

3. Consecutive angles are supplementary.

4. Regular polygon

6.4

MNOP is a rectangle with interior point A. If MA = 6x + 4 and PA = 7x – 4, find PN.

6.4

A

D C

B

5x +

8° 3x + 2°

6.4

Find x and y, such that ABCD is a rectangle.

6y + 2°

QRST is a rhombus. Find x and y, if m1 = y2 – 54, m2 = 5x + 7 and m3 = 7x – 1.

Q

R

T

S

23

6.4

1

Is ABCD a square, rectangle or rhombus?

D

A

C

Bx + 7

3y +

36.4

2x – 4

4y –

2

10z + 5°8z +

13°

GeometryGeometry

Homework:• 6.4 pgs. 351-

352 #16-38

• Chapter 6 Test Chapter 6 Test on Wednesdayon Wednesday

Every moment in planning saves 3 or 4 in execution.

Crawford Greenwalt