8.4 Rhombuses, Rectangles, and Squares
rhombus: a parallelogram with 4 congruent sides
rectangle: a parallelogram with 4 right angles
square: a parallelogram with 4 = sides and 4 right angles
Ex 1
Sometimes, always or never?
a) A rectangle is a square.
b) A square is a rhombus.
Ex 2
QRST is a square. What else do you know about
QRST?
Rhombus Corollary:
if it has
a quadrilateral is a rhombus if and only
Rectangle Corollary: a quadritateral is a rectangle if and
only if it has
Square Corollary: a quadrilateral is a square if and only if it is a
and a
Parallelograms
Ex 3 For any rhombus QRST, decide whether the
statement is always or sometimes true. Draw a sketch
and explain your reasoning.
a. ∠Q ≅ ∠S
b. ∠Q ≅ ∠R
Ex 4: Classify the special quadrilateral. Explain your
reasoning.
a.
70º
b.
Guided Practice
1. For any rectangle EFGH, is it always or sometimes true
that FG ≅ GH? Explain your reasoning.
2. A quadrilateral has four congruent sides and four
congruent angles. Sketch the quadrilateral and classify it.
Quiz tomorrow over 8.1 - 8.3
Homework:
Pages 537 - 540 # 1-7, 10-14, 16, 17, 25-29, 54
Thm 8.11
A parallelogram is a rhombus if and only if its
diagonals
A
B
Thm 8.12
C
A parallelogram is a rhombus if and only if each
diagonal bisects a pair of
D
A
B
D
C
Thm 8.13
A parallelogram is a rectangle if and only if its
diagonals
Ex 5
A
D
B
C
In
ABCD, the diagonals meet at a point E, and
AE = BE = 6. Is ABCD a rectangle? Explain.
Ex 6: Sketch rectangle ABCD. List everything you know
about it.
Ex 7: The diagonals of a rhombus WXYZ intersect at V.
Given that m∠XZY = 34º and WV = 7, find the
other indicated.
W
X
a. m∠WZV
7
V
b. m∠XYZ
34º
Z
Y
c. WY
d. XY
Pages 537 - 540 # 18, 20-23, 30-31, 32-50 even, 55-62, 65