Transcript Document

Lesson 8-4
Rectangles
5-Minute Check on Lesson 8-3
Transparency 8-4
Determine whether each quadrilateral is a parallelogram.
Justify your answer.
1.
2.
Determine whether the quadrilateral with the given vertices is a
parallelogram using the method indicated.
3. A(,), B(,), C(,), D(,) Distance formula
4. R(,), S(,), T(,), U(,) Slope formula
L
5. Standardized Test Practice: Which set of statements
will prove LMNO a parallelogram?
O
A
LM // NO and LO  MN
B
LO // MN and LO  MN
C
LM  LO and ON  MN
D
LO  MN and LO  ON
Click the mouse button or press the
Space Bar to display the answers.
M
N
5-Minute Check on Lesson 8-3
Transparency 8-4
Determine whether each quadrilateral is a parallelogram.
Justify your answer.
Yes, diagonal
bisect each other
1.
Yes, opposite
angles congruent
2.
Determine whether the quadrilateral with the given vertices is a
parallelogram using the method indicated.
3. A(,), B(,), C(,), D(,) Distance formula
4. R(,), S(,), T(,), U(,) Slope formula
Yes, opposite sides equal
No, RS not // UT
L
5. Standardized Test Practice: Which set of statements
will prove LMNO a parallelogram?
O
A
LM // NO and LO  MN
B
LO // MN and LO  MN
C
LM  LO and ON  MN
D
LO  MN and LO  ON
Click the mouse button or press the
Space Bar to display the answers.
M
N
Objectives
• Recognize and apply properties of rectangles
– A rectangle is a quadrilateral with four right angles
and congruent diagonals
• Determine whether parallelograms are
rectangles
– If the diagonals of a parallelogram are congruent,
then the parallelogram is a rectangle
Vocabulary
• Rectangle – quadrilateral with four right
angles.
Polygon Hierarchy
Polygons
Quadrilaterals
Parallelograms
Rectangles
Rhombi
Squares
Kites
Trapezoids
Isosceles
Trapezoids
Quadrilateral RSTU is a rectangle. If RT = 6x + 4 and
SU = 7x - 4 find x.
The diagonals of a rectangle are
congruent, so
Definition of congruent segments
Substitution
Subtract 6x from each side.
Add 4 to each side.
Answer: 8
Quadrilateral EFGH is a rectangle. If FH = 5x + 4 and
GE = 7x – 6, find x.
Answer: 5
Solve for x and y in the following rectangles
A
B
60°
8
Hint: Special Right Triangles
30°
D
C
y
A
D
A
B
C
B
2x
x
D
A
P = 36 feet
x
2x
C
x
3y
D
Hint: p is perimeter
Hint: 2 Equations, 2 Variables  Substitution
B
3x -9
2y
C
Quadrilateral LMNP is a rectangle. Find x.
MLP is a right angle, so
mMLP = 90°
Angle Addition Theorem
Substitution
Simplify.
Subtract 10 from each side.
Divide each side by 8.
Answer: 10
Quadrilateral LMNP is a rectangle. Find y.
Since a rectangle is a parallelogram, opposite sides are
parallel. So, alternate interior angles are congruent.
Alternate Interior Angles Theorem
Substitution
Simplify.
Subtract 2 from each side.
Divide each side by 6.
Answer: 5
Quadrilateral EFGH is a rectangle.
a. Find x.
b. Find y.
Answer: 7
Answer: 11
Kyle is building a barn for his horse. He measures the
diagonals of the door opening to make sure that they
bisect each other and they are congruent. How does
he know that the corners are
angles?
Answer: We know that
A parallelogram with
congruent diagonals is a rectangle. Therefore,
the corners are
angles.
Quadrilateral Characteristics Summary
Convex Quadrilaterals
Parallelograms
4 sided polygon
4 interior angles sum to 360
4 exterior angles sum to 360
Opposite sides parallel and congruent
Opposite angles congruent
Consecutive angles supplementary
Diagonals bisect each other
Rectangles
Trapezoids
Bases Parallel
Legs are not Parallel
Leg angles are supplementary
Median is parallel to bases
Median = ½ (base + base)
Rhombi
Angles all 90°
Diagonals congruent
All sides congruent
Diagonals perpendicular
Diagonals bisect opposite angles
Squares
Diagonals divide into 4 congruent triangles
Isosceles
Trapezoids
Legs are congruent
Base angle pairs congruent
Diagonals are congruent
Summary & Homework
• Summary:
– A rectangle is a quadrilateral with four right angles
and congruent diagonals
– If the diagonals of a parallelogram are congruent,
then the parallelogram is a rectangle
• Homework:
– pg 428-429; 10-13, 16-20, 42