Transcript Chapter 6.4-6.5

Chapter 6.4 and 6.5
Rectangles, Squares, and Rhombi
Rectangle
O A rectangle is a parallelogram with four right
angles.
Concept 1
Use Properties of Rectangles
CONSTRUCTION A rectangular garden gate is reinforced
with diagonal braces to prevent it from sagging. If JK = 12
feet, and LN = 6.5 feet, find KM.
Quadrilateral EFGH is a rectangle. If GH = 6 feet and FH
= 15 feet, find GJ.
A. 3 feet
B. 7.5 feet
C. 9 feet
D. 12 feet
Use Properties of Rectangles and Algebra
Quadrilateral RSTU is a rectangle. If mRTU =
8x + 4 and mSUR = 3x – 2, find x.
Quadrilateral EFGH is a rectangle. If mFGE =
6x – 5 and mHFE = 4x – 5, find x.
A. x = 1
B. x = 3
C. x = 5
D. x = 10
Concept 2
Matt is building a swimming pool in his backyard.
He measures the length and width of the pool so
that opposite sides are parallel. He also measures
the diagonals of the pool to make sure that they
are congruent. How does he know that the
measure of each corner is 90?
A.
Since opp. sides are ||, STUR
must be a rectangle.
B.
Since opp. sides are , STUR must
be a rectangle.
C.
Since diagonals of the are ,
STUR must be a rectangle.
D.
STUR is not a rectangle.
Rectangles and Coordinate Geometry
Quadrilateral JKLM has vertices J(–2, 3), K(1, 4),
L(3, –2), and M(0, –3). Determine whether JKLM is
a rectangle using the Distance Formula.
Step 1
Use the Distance
Formula to determine
whether JKLM is a
parallelogram by
determining if opposite
sides are congruent.
Quadrilateral WXYZ has vertices W(–2, 1), X(–1, 3), Y(3,
1), and Z(2, –1). Determine whether WXYZ is a rectangle
by using the Distance Formula.
A. yes
B. no
C. cannot be
determined
Rhombus
O A rhombus is a parallelogram with all four
sides congruent.
Concept 1
Use Properties of a Rhombus
A. The diagonals of rhombus WXYZ intersect at V.
If mWZX = 39.5, find mZYX.
Use Properties of a Rhombus
B. ALGEBRA The diagonals of rhombus WXYZ intersect at
V. If WX = 8x – 5 and WZ = 6x + 3, find x.
A. ABCD is a rhombus. Find mCDB if
mABC = 126.
A. mCDB = 126
B. mCDB = 63
C. mCDB = 54
D. mCDB = 27
B. ABCD is a rhombus. If BC = 4x – 5 and
CD = 2x + 7, find x.
A. x = 1
B. x = 3
C. x = 4
D. x = 6
Square
O A square is a parallelogram with four
congruent sides and four right angles.
Concept 3
Concept
Use Conditions for Rhombi and
Squares
GARDENING Victor is measuring the boundary of a new
garden. He wants the garden to be square. He has set
each of the corner stakes 6 feet apart. What does Victor
need to know to make sure that the garden is square?
Ariel has a shape he knows to be a parallelogram and all
four sides are congruent. Which information does he need
to know to determine whether it is also a square?
A. The diagonal bisects a pair of
opposite angles.
B. The diagonals bisect each other.
C. The diagonals are perpendicular.
D. The diagonals are congruent.
Classify Quadrilaterals Using Coordinate Geometry
Determine whether parallelogram ABCD is a rhombus, a
rectangle, or a square for A(–2, –1),
B(–1, 3), C(3, 2), and D(2, –2). List all that apply. Explain.
Determine whether parallelogram EFGH is a rhombus, a
rectangle, or a square for E(0, –2),
F(–3, 0), G(–1, 3), and H(2, 1). List all that apply.
A. rhombus only
B. rectangle only
C. rhombus, rectangle, and
square
D. none of these