{{asɛmtiNe Ɔkyerɛwfo}} | Nhomakorabea | Nneɛma a ɛma wotumi yɛ ade

1

Quadrilateral Family Tree

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Using the applet on the previous slide, determine the properties of rectangles. Since a rectangle is a parallelogram, it will have all SIX parallelogram properties. A rectangle will also have an additional TWO "special" properties that distinguishes them from other parallelograms

Only one pair of opposite sides parallel
Only one pair of opposite sides congruent
A diagonal divides the parallelogram into two congruent triangles
Diagonals bisect its angles
Diagonals are congruent.
4 right angles (Equiangular quadrilateral)
Diagonals are perpendicular.
Both pairs of opposite sides are congruent
Equilateral quadrialteral
Diagonals bisect each other
Both pairs of opposite sides are parallel
Consecutive angles are supplementary
Both pairs of opposite angles are congruent

6 Properties of Parallelograms that rectangles have
2 Special (additional) Properties of Rectangles

Textbooky Notes for Rectangles (summary of everything we have discovered thus far)

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Lookout Alert!! When both diagonals of a rectangle are drawn, pay close attention to the 4 resulting "non"-overlapping triangles formed.

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In Rectangle QRST,

,

, and

are

1

In Rectangle QRST, which of the following statements MUST BE TRUE?

True Statement

Lookout Alert #2!!! RIGHT TRIANGLE APPLICATIONS when given a RECTANGLE.

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A diagonal of a rectangle divides the rectangle into 2 triangles.

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List some right triangle applications, you might be able to apply when given a diagonal of a rectangle.

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In Rectangle QRST,

and

.

Find the following:

a)

b) Perimeter of QRST =

c) m

d) m

*Round to the nearest tenth.

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In Rectangle WXYZ, m

;

.

Find:

a) m

b)

c)

d) Perimeter of WXYZ=

*Round to nearest tenth.

1

In Rectangle QRST,

and

.

Find the following:

a)

b) Perimeter of

=

c) m

d) m

*Round to the nearest tenth.

1

In Rectangle WXYZ, m

;

.

Find:

a) m

b)

c)

d) Perimeter of WXYZ=

*Round to nearest tenth.

1

If ABCD is a rectangle, find the values of:

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Always, Sometimes , Never:

a) A parallelogram is a rectangle.

b) The diagonals of a parallelogram are congruent.

c) The diagonals of a rectangle bisect each other.

d) The diagonals of a rectangle are congruent.

e) A parallelogram is equiangular.

Mmuae Afoforo a Wobɛpaw:

sometimes

never

always

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QRST is a rectangle. Which of the following statements are (ALWAYS) TRUE?

comp.
m
m
m
m
comp.

True Statement
Not (necessarily) True

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ABCD is a rectangle with diagonals

and

intersecting at E.

If

and

, then

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ABCD is a rectangle with diagonals

and

intersecting at E.

If

, then

1

ABCD is a rectangle with diagonals

and

intersecting at E.

If

and

, then

1

ABCD is a rectangle with diagonals

and

intersecting at E.

If

and

, then

1

ABCD is a rectangle with diagonals

and

intersecting at E.

If m

, find:

m

1

ABCD is a rectangle with diagonals

and

intersecting at E.

Which triangles are congruent?

Mmuae Afoforo a Wobɛpaw:

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ABCD is a rectangle with diagonals

and

intersecting at E.

If m

and

, find:

m

1

LMNP is a rectangle with diagonals

and

intersecting at F.

If m

and m

, find:

m

1

LMNP is a rectangle with diagonals

and

intersecting at F.

If m

and m

, find:

m

1

METS is a rectangle with diagonals

and

intersecting at Q.

If m

and m

, find:

m

1

YANK is a rectangle with diagonals

and

intersecting at S.

If

,

, and m

, find:

m

*Round to nearest tenth.

1

NDFB is a rectangle with diagonals

and

intersecting at W.

If

,

, and m

, find:

m

Perimter of NDFB =

*Round to nearest tenth.

Three Major ways to prove a Parallelogram is a Rectangle*

*Must first prove/state that quadrilateral is a parallelogram then use the following to prove that the parallelogram is a rectangle.

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When using coordinate geometry to prove that a quadrilateral is a rectangle:
STEP 1 - Find the SLOPE of all 4 sides.
STEP 2 - Prove that quad is a parallelogram by showing that both pairs of opposite sides are parallel (2 sets of equal slopes)
STEP 3 - Prove that parallelogram is a rectangle by showing one of its angles is a right angle (show that the slopes of one pair of consecutive sides are negative reciprocals --> perpendicular --> form right angles)
Example: Quadrilateral READ has vertices with coordinates R(−1,3), E(2,7), A(10,1), and D(7,−3). Prove READ is a rectangle. [The use of the set of axes below is optional.]

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The coordinates of the vertices of quadrilateral HYPE are H(−3,6), Y(2,9), P(8,−1), and E(3,−4). Prove HYPE is a rectangle. [The use of the set of axes below is optional.]

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The coordinates of the vertices of quadrilateral ABCD are A(0,4), B(3,8), C(8,3), and D(5,−1). Prove that ABCD is a parallelogram, but not a rectangle. [The use of the set of axes below is optional.]

1

The vertices of quadrilateral MATH have coordinates M(−4,2), A(−1,−3), T(9,3), and H(6,8). Prove that quadrilateral MATH is a parallelogram. Prove that quadrilateral MATH is a rectangle. [The use of the set of axes below is optional.]

Lesson 4 Rectangles

Textbooky Notes for Rectangles (summary of everything we have discovered thus far)

Lesson 4 Rectangles

Quadrilateral Family Tree

Using the applet on the previous slide, determine the properties of rectangles. Since a rectangle is a parallelogram, it will have all SIX parallelogram properties. A rectangle will also have an additional TWO "special" properties that distinguishes them from other parallelograms

6 Properties of Parallelograms that rectangles have

2 Special (additional) Properties of Rectangles

Textbooky Notes for Rectangles (summary of everything we have discovered thus far)

In Rectangle QRST, which of the following statements MUST BE TRUE?

List some right triangle applications, you might be able to apply when given a diagonal of a rectangle.

QRST is a rectangle. Which of the following statements are (ALWAYS) TRUE?

Three Major ways to prove a Parallelogram is a Rectangle*

The coordinates of the vertices of quadrilateral HYPE are H(−3,6), Y(2,9), P(8,−1), and E(3,−4). Prove HYPE is a rectangle. [The use of the set of axes below is optional.]

The coordinates of the vertices of quadrilateral ABCD are A(0,4), B(3,8), C(8,3), and D(5,−1). Prove that ABCD is a parallelogram, but not a rectangle. [The use of the set of axes below is optional.]

The vertices of quadrilateral MATH have coordinates M(−4,2), A(−1,−3), T(9,3), and H(6,8). Prove that quadrilateral MATH is a parallelogram. Prove that quadrilateral MATH is a rectangle. [The use of the set of axes below is optional.]

Quadrilateral Family Tree

Using the applet on the previous slide, determine the properties of rectangles. Since a rectangle is a parallelogram, it will have all SIX parallelogram properties. A rectangle will also have an additional TWO "special" properties that distinguishes them from other parallelograms

6 Properties of Parallelograms that rectangles have

2 Special (additional) Properties of Rectangles

In Rectangle QRST, which of the following statements MUST BE TRUE?

List some right triangle applications, you might be able to apply when given a diagonal of a rectangle.

QRST is a rectangle. Which of the following statements are (ALWAYS) TRUE?

Three Major ways to prove a Parallelogram is a Rectangle*

The coordinates of the vertices of quadrilateral HYPE are H(−3,6), Y(2,9), P(8,−1), and E(3,−4). Prove HYPE is a rectangle. [The use of the set of axes below is optional.]

The coordinates of the vertices of quadrilateral ABCD are A(0,4), B(3,8), C(8,3), and D(5,−1). Prove that ABCD is a parallelogram, but not a rectangle. [The use of the set of axes below is optional.]

The vertices of quadrilateral MATH have coordinates M(−4,2), A(−1,−3), T(9,3), and H(6,8). Prove that quadrilateral MATH is a parallelogram. Prove that quadrilateral MATH is a rectangle. [The use of the set of axes below is optional.]