Geometry

Today:• Over 6.4

Vocab• 6.4

Instruction• Practice

Every moment in planning saves 3 or 4 in execution.

Crawford Greenwalt

Assignment:– 6.4 Intro WS

Geometry

Every moment in planning saves 3 or 4 in execution.

Crawford Greenwalt

1.

2.

3.

4.

5.

REVIEW:

What are the properties of a parallelogram?

6.3

6.4 Rhombuses, Rectangles, & Squares

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

parallelograms

Vocabulary:square, rhombus, rectangle

vocabulary

Rectangle – a quadrilateral with 4 right angles

6.4

Facts about a rectangle.

Has ALL properties of a parallelogramHas four right angles.

-Diagonals are congruent.

A parallelogram is a rectangle iff the diagonals are congruent.

6.47 Properties

vocabulary

Rhombus: a quadrilateral with 4 congruent sides

6.4

Facts about a rhombus.

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

diagonals are perpendicular.

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

6.4

Has ALL properties of a parallelogramHas four congruent sides.

8 Properties

vocabulary

Square – a quadrilateral with 4 right angles and 4 congruent sides – it is both a rhombus and a rectangle

6.4

Facts about a square.

Has ALL properties of a parallelogram

Has ALL properties of a rectangle.

6.4

10 Properties

Has ALL properties of a rhombus.

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?

• Rectangle

• Parallelogram

A B

CD

Questions about special quadrilaterals.

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 rhombus

6.4

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 quadrilaterals.

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 +

3

6.4

2x – 4

4y –

2

10z + 5°8z + 13°

Assignment:– 6.4 p 351 #

16-38– Test Chapter 6

on Wednesday

GeometryEvery moment in planning saves 3 or 4 in execution.

Crawford Greenwalt