The document provides information about properties of kites, trapezoids, triangles, and midsegments. It defines key properties such as: - Kites have two pairs of congruent adjacent sides and perpendicular diagonals. - Trapezoids have one pair of parallel sides and two sets of supplementary angles. Isoceles trapezoids have congruent base angles. - Midsegments of triangles and trapezoids are parallel to the third side and have a length that is half of the third side. - Triangles can be divided into smaller congruent triangles using midsegments.

1. 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.
m b a 100°
c
f
e
g d n
h
a= 80°, b= 20°, c=160°, d=20 °, e=80°, f=80°, g=110°, h=70°, m=110°,
n=100°

2. What your answer should look like...
Statement Reason
a= 80 ° Linear Pair with 100°
b= 20° Isoceles Triangle Conjecture
c= 160° Linear Pair with angle b
d= 20° Correseponding Angles with angle b
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.

3. 5.3 Kites and their properties...
By now you should know kites...
1. are quadrilaterals
2. have interior angle sums of 360°
3. are the ONLY quarilateral that has adjacent congruent
sides

4. 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 diagonal
5. the Vertex angles are bisected

5. 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!!

6. Try it....
1. 3.
b 40° 6
a 65° d
e b 72°
110°
2. c
x a
Perimeter is 20.
4 Perimeter is 40.

7. 5.3 Trapezoid properties...
You should know....
Trapezoids ...
1. are quadrilaterials
2. have an interior angle sum of 360°
3. one pair of parallel sides (the bases)
4. 2 sets of bases angles

8. Trapezoids.....
1. consecutive angles that are supplemetary
2 angles + = 180° 2 angles + = 180°
180 + 180 = 360°

9. 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
triangles
a) ones on left and right are ≅
b) ones on top an bottom are NOT≅ but are iscocelses Δ's

10. You know what else....
I bet I can fold an Isocseles Trapezoid and pieces will
match up!!! That way I know which parts are ≅ !

11. Try some...
2. c
1. a b
b
42° 91°
a 55°
3. x
c
a
50° Perimeter is 100.
40
10
b
d

12. 5.5 Midsegement Properties
Midsegment 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.....

13. 2
4 3
1
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, 3 are all ≅ AND face the same direction
4 must fe Flipped and rotated to fit

14. 1. b
a
70°
40° c 2.
x
6 z
10 y
5

15. 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
Wow those Δ's have the same angle
10
Neato-
that is a
transversal
in that
trapezoid!
20
Hey-one BIGΔ, one littleΔ and a trapezoid!

16. Interesting...
I bet trapezoids have midesegments too and I bet they
are parallel to the bases!!!
10 midsegment = b1 + b2
2
20
30
OH wait!!
I bet to get the length of the midsegment all I have to
do is average the bases!

17. 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).

18. Red segments are midsegments
Try these..
60
1. y 2.
14 a
16
x 40
c
z 20 110°
b
3. 4. Isoceles Trapezoid
a c 2 10
b
4 b 40° d
80°
a c
50

19. 14.
n
m k
a b
g
54¡ c e f i
d
h