1
Lesson Plan #57
Class: Geometry
Date: Monday February 6th, 2017
Topic: Kite
Aim: What are some properties of a kite?
Objectives:
1) Students will be able to develop the properties of a kite
2) Students will be able to find missing side lengths and angles measures using properties of kites.
3) Students will be able to find area and perimeter of kites.
4) Students will be able to describe rigid motions with kites on the plane and coordinate plane.
5) Students will be able to answer population density questions with kites
HW #57:
Page 193 #’s 28-29
Do Now 1: A rancher has 100 feet of fencing to enclose a rectangular cattle area. Which dimensions would result in the largest
area for this cattle area?
A) The length 10 more than the width
B) The length 5 more than the width
C) The length and the width equal
D) As long as the amount of fencing stays constant, the area will be constant.
Do Now 2:
1) Mark a point in the center of the open space at the
right. Mark this point as O. Using point O, construct
a circle.
2) Construct a diameter through point O. Label the
diameter as AB .
3) Construct the perpendicular bisector of AB .
4) Label the intersection points of the circle and
The perpendicular bisector of AB as
CD
5) What figure is formed by connecting points
A, C, B, D and back to A, in that order?
_____________________________________
PROCEDURE:
Write the Aim and Do Now
Get students working!
Take attendance
Give Back HW
Collect HW
Go over the Do Now
Assignment #1: Discuss in your groups:
At the right we have a kite, which is defined as a quadrilateral
with two distinct pairs of adjacent sides that are congruent.
Draw in the diagonals of the kite.
What can you state about the diagonals of a kite?
Why?
What are some other properties of a kite that can be proven? Do not write out the proofs; just plan them!
2
Summary of the properties of a kite:
The diagonals are perpendicular.
The longer diagonal bisects the shorter diagonal.
The longer diagonal bisects opposite angles (vertex angles).
ONE pair of opposite congruent angles.
1
d1  d 2
2
The area of the kite is
Sample Test Questions:
1)
2) A) Find the area of the kite at the right. Find the perimeter of the kite at right
Area =
Perimeter =
3) In Kite YDOC at the right, the length of diagonal CD is 24 cm, and the length of diagonal
YO is represented by 12 x  5 y .
4) Find a rigid motion or sequence of rigid motions that map
ABC onto ADC .
3
5) Given that quadrilateral ABCD at the right is a kite:
A) Draw in diagonal AC. Label the intersection of the diagonals E.
B) Find
 


rBD C  _____ TAB  A ______ RE ,180o EC _________ rAB TDA D  ________
C) If AB = 6 and m<ABC = 60o, find:
AC _____ BC ______ AE ______ CE _________ BE ______
D) Describe a precise sequence of rigid motions that would show ABD  CBD
E) Given the information from part C above, if DE = 6, find
Area of kite ABCD _____
AD ________
CD __________
perimeter of kite ABCD _______
6) The two kites at the right represent two pens for cats.
Pen JKLM will hold 20 cats. Pen ABCD will hold 10 cats.
Which pen has the greater population density?
7) Kite ABCD is graphed at the right.
A) What is the area of kite ABCD?
o
B) When kite ABCD is rotated 90 in a clockwise direction about the origin, its
image is kite A’B’C’D’. Is distance preserved under this rotation? Explain.
C) What are the coordinates of point A’?
D) Kite ABCD is dilated with a constant of dilation of 3 with the origin as the center
of dilation producing image A’’B’’C’’D’’. What are the coordinates of D’’?
8) A)Kite CDEF is inscribed in circle A. Find the area of the shaded region.
3
5
B) Find ratio of the area of quadrilateral ADCF to quadrilateral ADEF.
A)
B)
4
9) Mike bought 1000 square meters of fabric to make kites with the indicated dimensions.
How many complete kites can he make with the fabric?
10) Construct the angle bisector of  BAD in kite ABCD at the right
If enough time:
1)
2)
5)
6)
5
7)
7)
8)
9)