Download chapter 5: quadrilaterals

CHAPTER 5:
QUADRILATERALS
5-4:
Special Quadrilaterals
RECTANGLES
A rectangle is a quadrilateral that has four
right angles.
Because both pairs of opposite angles of a
rectangle are congruent, a rectangle is a
parallelogram.
RHOMBUS
A rhombus is a quadrilateral that has four
congruent sides.
Because both pairs of opposite sides of a rhombus are
congruent, every rhombus is a parallelogram.
SQUARE
A square is a quadrilateral with four right
angles and four congruent sides.
Because both pairs of opposite angles and sides are
congruent, all squares are parallelograms.
THEOREM 5-12
THEOREM 5-12
The diagonals of a rectangle are congruent.
THEOREM 5-13
THEOREM 5-13
The diagonals of a rhombus are perpendicular.
THEOREM 5-14
THEOREM 5-14
Each diagonal of a rhombus bisects two angles
of the rhombus.
THEOREM 5-15
THEOREM 5-15
The midpoint of the hypotenuse of a right
triangle is equidistant from the three vertices.
THEOREM 5-16
THEOREM 5-16
If an angle of a parallelogram is a right angle,
then the parallelogram is a rectangle.
THEOREM 5-17
THEOREM 5-17
If two consecutive sides of a parallelogram are
congruent, then the parallelogram is a
rhombus.
ALWAYS, SOMETIMES, NEVER
1. A square is ______ a rhombus.
2. The diagonals of a parallelogram
______ bisect the angles of the
parallelogram.
3. A quadrilateral with one pair of
sides congruent and one pair
parallel is ______ a
parallelogram.
4. The diagonals of a rhombus are
______ congruent.
1. Always
2. Sometimes
3. Sometimes
4. Sometimes
ALWAYS, SOMETIMES, NEVER
1. A rectangle ______ has
consecutive sides congruent.
2. A rectangle ______ has
perpendicular diagonals.
3. The diagonals of a rhombus
______ bisect each other.
4. The diagonals of a
parallelogram are ______
perpendicular bisectors of
each other.
1. Sometimes
2. Sometimes
3. Always
4. sometimes
A
Quadrilateral ABCD is a Rhombus.
Find the measure of each angle.
D
1.
ACD
1. 62
2.
DEC
2. 90
3.
EDC
3. 28
4.
ABC
4. 56
B
E
62
C
Quadrilateral MNOP is a rectangle.
M
N
29
Complete:
12
L
P
1. m
PON =
1. 90
2. m
PMO =
2. 61
3. PL =
3. 12
4. MO =
4. 24
O
∆ABC is a right ∆; M is the midpoint of AB.
A
M
C
B
1. If AM = 7, then MB = _____, 1. 7, 14, 7
AB = _____, and CM =
_____.
2. x/2, x/2, x/2
2. If AB = x, then AM = _____,
MB = _____, and MC =
_____.
CLASSWORK/HOMEWORK
• Pg. 186, Classroom Exercises 1-11
• Pg. 187, Written Exercises 2-18 even.