Download 5.3 and 5.4 notes - Rambo-math

GEO WARM UP:
COPY AND SOLVE for x THEN find each angle
Signed interim?? Get it out-­-­ will collect
New stuff today......
QUIZ next week.....5.3 to 5.4
5.3 Kites and their properties...pg. 266
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
NOW take that kite you drew and ADD to the picture
what you can figure out from the gold boxes on page
267......
This is ONE thing to add....
Kites also....
1. have a set of Nonvertex angles that are ≅ c-35
2. have a set of Vertex angles that are NOT ≅
3. have 2 diagonals that are perpendicular to each other c-36
4. the shorter diagonal is bisected by the other diagonal c-37
5. the Vertex angles are bisected c-38
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!!
IN ADDITON.... What shapes are formed by the
diagonals?
Try it....
1.
3.
b
a
40°
d
e
65°
110°
x
Perimeter is 20.
4
72°
b
c
2.
6
a
Perimeter is 40.
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
Trapezoids.....
1. consecutive angles that are supplemetary c-39
Isoceles trapezoids are special....
What charactersitics do they have?
Isoceles Trapezoids are special...
They have ALL the properties of a trapezoid AND....
1. Their base angles are ≅ c-40
2. The NON-parallel sides are ≅
3. The diagonals are ≅ WHICH cut the trapezoid into 4 c-41
triangles
a) 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.
a
b
91°
42°
3.
c
a
b
55°
x
a
40
50°
10
b
d
c
Perimeter is 100.
HW answers pg. 269 # 1-6
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.....
2
4
3
1
You get ONE giant triangle that is divided into 4 little
triangles --all of which are ≅ to each other. c-42
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
b
1.
70°
a
40°
c
2.
x
z
6
10
5
y
Hey--that midsegment is Parallel to the third side
(one not touching)
Guess what?--The measure of that midesgment is c-41
HALF of the third side
Wow those Δ's have the same angl
Neatothat is a
transversal
in that
trapezoid!
10
20
Hey-one BIGΔ, one littleΔ and a trapezoid!
Interesting...
I bet trapezoids have midesegments too and I bet they
are parallel to the bases!!!
midsegment = b1 + b2
10
2
20
30
OH wait!!
I bet to get the length of the midsegment all I have to
do is average the bases!
c-44
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).
Red segments are midsegments
Try these..
1.
y
14
16
2.
60
a
x
c
20
z
40
110°
b
3.
a
4. Isoceles Trapezoid
10
b
c 2
4
80°
b
40°
d
a
c
50
GEO WU-WRITE THIS IN YOUR NOTES
Triangle midsegment Theorem:
Midsegment is half the base it is parallel to
Midesegment is parallel to base
Midsegment connects midpoints of sides
trapezoid midsegment theorem:
Midsegment is parallel to base
Midsegment connects midpoints of sides
Midsegment is the average of the 2 bases
HW answers pg. 275 # 1-7