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5.3 Kite and Trapezoid Properties pg. 266 to 271
Warm up : pg 272 # 17 AND explain in complete sentences how you arrived from on answer to the next
17.ab
c
d
e
f
g
h
m
n
a= 80°, b= 20°, c=160°, d=20 °, e=80°, f=80°, g=110°, h=70°, m=110°, n=100°
100°
What your answer should look like...
a= 80 ° b= 20°c= 160°d= 20°
Statement Reason
OR
Angle a equals 80 ° because it forms a linear pair with the 100° angle because to have a linear pair 2 angles must add to equal 180°. This angle is part of an Isoceles triangle becasue of the tick marks. It is one of the base angles therefore the other base angle is 80°. If both angles are added and then subtracted from 180° because that is the sum of the angles of a triangle then the result is 20° for angle b. Angle b forms a linear pair with angle c so if you subtract the 20° from 180° you are left with 160° for angle c.
Linear Pair with 100°Isoceles Triangle ConjectureLinear Pair with angle bCorreseponding Angles with angle b
5.3 Kites and their properties...
By now you should know kites...1. are quadrilaterals2. have interior angle sums of 360°3. are the ONLY quarilateral that has adjacent congruent
sides
Kites also....1. have a set of Nonvertex angles that are ≅2. have a set of Vertex angles that are NOT ≅3. have 2 diagonals that are perpendicular to each other 4. the shorter diagonal is bisected by the other diagonal5. the Vertex angles are bisected
If you forget what parts are congruent...
Think of it this way....
If you FOLD a kite down the middle (line of reflection), all the ≅ pieces will match up!!
Try it....
a
b
110°
65°
4
6
Perimeter is 20.
1.
2.
3.
x a
40°
b
c
de
Perimeter is 40.
72°
5.3 Trapezoid properties...
You should know....
Trapezoids ...1. are quadrilaterials2. have an interior angle sum of 360°3. one pair of parallel sides (the bases)4. 2 sets of bases angles
Trapezoids.....1. consecutive angles that are supplemetary
2 angles + = 180° 2 angles + = 180°
180 + 180 = 360°
Isoceles Trapezoids are special...
They have ALL the properties of a trapezoid AND....1. Their base angles are ≅2. The NON-parallel sides are ≅3. The diagonals are ≅ WHICH cut the trapezoid into 4
trianglesa) ones on left and right are ≅b) ones on top an bottom are NOT≅ but are iscocelses Δ's
You know what else....
I bet I can fold an Isocseles Trapezoid and pieces will match up!!! That way I know which parts are ≅ !
Try some...
1.2.
3.
a b
42° 91°a
bc
a
b
c
d
50° Perimeter is 100.
1040
x
55°
5.5 Midsegement PropertiesMidsegment is a segment connecting 2 midpoints of 2 NON parallel sides.
You rememeber that right?1. Every side has a midpoint.2. Each midpoint can connect to 2 sides that are NOT parallel.3. The midsegment is Parallel to the third side (one it DOES NOT touch)
If you combine these three diagrams into one.....
You get ONE giant triangle that is divided into 4 little triangles --all of which are ≅ to each other.
Note: sometimes the little triangle in the middle must be rotated to match up with the others
1
2
34
1, 2, 3 are all ≅ AND face the same direction4 must fe Flipped and rotated to fit
a
b
c40°
1.
2.
5
x
6 z
y10
70°
Hey--that midsegment is Parallel to the third side (one not touching)
Guess what?--The measure of that midesgment is HALF of the third side
10
20
Hey-one BIGΔ, one littleΔ and a trapezoid!
Wow those Δ's have the same angle
Neato-that is a transversal in that trapezoid!
Interesting...
I bet trapezoids have midesegments too and I bet they are parallel to the bases!!!
OH wait!!I bet to get the length of the midsegment all I have to do is average the bases!
10
20
30
midsegment = b1 + b22
So wait....
The bigΔ can be divided into a little Δ and a trapezoid (blue).
Then I could also divide that trap into 2 more trapezoids (red).
Try these..
1416
20
x
y
z
1. 2.
3.
a
b
c
60
40
2
4
a
b
c
80°
4. Isoceles Trapezoid10
50
40°
a
b
d
Red segments are midsegments
110°
c
14.
a b
c
d
e f
g
h
i
km
n
54¡
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