Transcript Lesson 6-4 - DavisEric.com

Lesson 6-4
Rectangles
• Recognize and apply properties of rectangles.
• Determine whether parallelograms are rectangles.
• rectangle
Standard 7.0 Students prove and use
theorems involving the properties of
parallel lines cut by a transversal, the
properties of quadrilaterals, and the
properties of circles. (Key)
Rectangle
• Def—A //ogram with 4 Right Angles
Properties of a Rectangle
• Rectangle  Diagonals are 
• (Also has all the properties of a //ogram.)
–Opposite sides 
–Opposite angles 
–Consecutive angles supplementary
–Diagonals bisect each other
A
D
E
Given ABCD is a Rectangle, list
B
everything that must be true.
AB // CD AD // BC
mA  mB  mC  mD  90
AC  BD
C
//ogram: Opp. Sides //
Def: 4 rt. s
#1: Diagonals are 
#2: Opp. Sides are 
#3: Opp. s are 
#4: Consec. s are Supp.
#5: Diagonals bisect each other.
AB  CD
AD  BC
AE  EC DE  EB
Diagonals of a Rectangle
Quadrilateral RSTU is a rectangle. If
RT = 6x + 4 and SU = 7x – 4, find x.
Diagonals of a Rectangle
The diagonals of a rectangle are congruent,
Diagonals of a rectangle are .
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.
A. x = –1
B. x = 3
C. x = 5
D. x = 10
A.
B.
C.
D.
A
B
C
D
Angles of a Rectangle
Quadrilateral LMNP is a rectangle. Find x.
Angles of a Rectangle
Angle Addition Postulate
Substitution
Simplify.
Subtract 10 from each
side.
Divide each side by 8.
Answer: 10
Quadrilateral EFGH is a rectangle. Find x.
A. 6
B. 7
C. 9
D. 14
1.
2.
3.
4.
A
B
C
D
Reminder
• Perpendicular lines have opposite
reciprocal slopes.
– Prove the sides of a quadrilateral are
perpendicular and you have proven it is
a rectangle.
Rectangle on a Coordinate Plane
Quadrilateral ABCD has vertices A(–2, 1), B(4, 3),
C(5, 0), and D(–1, –2). Determine whether ABCD
is a rectangle using the Slope Formula.
Method 1: Use the Slope Formula,
to see if
opposite sides are parallel and consecutive sides are
perpendicular.
Rectangle on a Coordinate Plane
= Slopes  // lines
Opp. Reciprocal
Slopes   lines
//ogram with 4 right
angles  Rectangle
Rectangle on a Coordinate Plane
Method 2: Use the Distance Formula,
to determine whether opposite
sides are congruent.
Rectangle on a Coordinate Plane
Find the length of the diagonals.
//ogram w/  Diagonals
 Rectangle
Opp. Sides   //ogram
Quadrilateral WXYZ has vertices W(–2, 1),
X(–1, 3), Y(3, 1), and Z(2, –1). Determine
whether WXYZ is a rectangle using the
Distance Formula.
A. yes
B. no
C. cannot be
determined
1.
2.
3.
A
B
C
Quadrilateral WXYZ has vertices
W(–2, 1), X(–1, 3), Y(3, 1), and Z(2, –1).
What are the lengths of diagonals WY and XZ?
A.
B. 4
C. 5
D. 25
A.
B.
C.
D.
A
B
C
D
Homework
• pg 344:
1, 2, 7, 8, 10, 13-21,
27-29