3.5 what are special parallelograms? pg. 20 properties of rhombi, rectangles, and squares
TRANSCRIPT
3.5
What Are Special Parallelograms?
Pg. 20Properties of Rhombi, Rectangles, and Squares
3.5 – What Are Special Parallelograms?___Properties of Rhombi, Rectangles, and Squares
In the previous lesson, you learned that parallelograms have both pairs of opposite sides parallel. You also discovered many different properties of parallelograms. Today you are going to continue your investigation with parallelograms with even more special properties.
3.28 –PARALLELOGRAMS WITH RIGHT ANGLESMark's favorite shape is a parallelogram with four right angles. a. What is the name of Mark's shape? Draw a picture to support your answer.
rectangle
b. What do you already know about this shape since it is a parallelogram?
Both _____________
sides are ________________
opposite
parallel
Both _____________ sides are
________________
opposite
congruent
Both _____________ angles are
________________
opposite
congruent
Both _____________ angles are
________________
consecutive
supplementary
The diagonals ________________ each other
bisect
c. Mark wanted to learn more about his shape. He noticed that the diagonals seem to have a special relationship beyond just being bisected. He decided to investigate. He drew a rectangle twice, adding one diagonal. Find the length of AC and BD. Show all work. What do you notice?
82 + 152 = x2
289 = x2
17 = x
82 + 152 = x2
289 = x2
17 = x
Diagonals are congruent
3.29 –PARALLELOGRAMS WITH EQUAL SIDESAudrey has a favorite quadrilateral is a parallelogram that has four equal sides. a. What is the name of Audrey's shape? Draw a picture to support your answer.
Rhombus
b. What do you already know about this shape since it is a parallelogram?
Both _____________
sides are ________________
opposite
parallel
Both _____________ sides are
________________
opposite
congruent
Both _____________ angles are
________________
opposite
congruent
Both _____________ angles are
________________
consecutive
supplementary
x y
xy
x y 180
The diagonals ________________ each other
bisect
c. Audrey wanted to learn more about her shape. She noticed that the diagonals seem to have a special relationship as well. She measured the sides of the rhombus and all were 5 units long. Then she measured AC = 6 units and BD = 8 units. Mark these lengths on the picture below. Is there a way to tell if ∆AEB is a right triangle? Explain.
5
5
5
5 334
4
32 + 42 = 52
9 + 16 = 2525 = 25
The diagonals are perpendicular
d. Audrey noticed something else with the angle in the rhombus. Using the given lines symmetry, mark any angles congruent. What do you notice?
Diagonals bisect the angles
3.30 –PARALLELOGRAM S WITH EQUAL SIDES AND RIGHT ANGLESMs. Matthews has a favorite quadrilateral is a parallelogram that has four right angles and four equal sides. a. What is the name of Ms. Matthews' shape? Draw a picture to support your answer.
square
b. A square has more properties than any other quadrilateral. Why do you think this is?
It is a parallelogram, a rectangle, and a rhombus
3.31 – SPECIAL PARALLELOGRAMSName the type of parallelogram. Explain how you know using only the markings.
rhombus rectangle rhombus
parallelogram rectangle square
3.32 – MISSING PARTSFind the missing information based on the type of shape and its special properties.
a. The diagonals of rhombus PQRS intersect at T. Find the indicated measure. _____
_________
_________
RP = _________
SP = _________
RS = _________
1530°
30°
90°90°
60°
60°
12
1515
mQPR
mQTP
mPQT
b. The diagonals of rectangle WXYZ intersect at P. Given that XZ = 12, find the indicated measure.
_________ _________ _________ WP = _________
40° 40°
50°50°
80°
80°
6
WXZ
PYX
XPY
c. The diagonals of square DEFG intersect at H. Given that EH = 5, find the indicated measure.
HF =
90°
90°
45°
45°45°
45°
5
GHF
HGF
HFG