Download midsegment - Shope-Math

Geometry 10 December 2012
1) Place your book and binder on your desk.
2) Put papers from folder into in your binder.
3) WARM UP
a) Do proof “strip”
b) Do Investigation 1, page 275
- draw a triangle on patty paper
- pinch each side to find midpoints
- draw mid-segments
- copy one small triangle on 2nd patty paper
- compare triangles
objective
Students will explore and apply polygon
properties.
students will work collaboratively to do
investigations, write conjectures and apply
properties to solve problems.
due Tuesday
5.4: 2, 3, 4, 7
5.5: 1, 2, 3, 5, 6
5.6: 11, 12, 13
TEST- proofs, polygon properties
Wednesday/ Thursday
Semester Review Packet due on your final exam
day
P2- Monday, December 17
P3- Tuesday, December 18
P5 and P6- Wednesday, December 19
Kite Properties
Isosceles Trapezoids
PQRS is an isosceles trapezoid. Find m<P, m<Q,
and m<R.
S
50°
P
m<R= 50⁰
R
>
>
Q
base angles are congruent
m<Q= m<P= 180 – 50 = 130º
consecutive angles are
supplementary
check: 2(50) + 2(130) = 100 + 260 = 360√
A midsegment of a triangle is
a segment connecting the
midpoints of two sides of a
triangle
Y
R
X
T
Z
Triangle Midsegments
Continue with investigation 1….
- compare angles
what can you conclude about the
mid-segment and the third side?
- compare length of mid-segment with the
length of the 3rd side
what can you conclude?
Triangle Midsegment
The segment connecting the midpoints of two
sides of a triangle is parallel to the 3rd side and
X
is half as long.
1
YZ || RT and RT  YZ
2
Z
T
R
Y
Mid-segments of a trapezoid
Watch video:
http://www.youtube.com/watch?v=O2bf1mZQ
WXI
http://math.kendallhunt.com/x19429.html
Shope Demo with Patty Paper Trapezoids
Midsegment of a trapezoid
• The midsegment of a
trapezoid is the
B
segment that connects
the midpoints of its
legs.
C
midsegment
A
D
Midsegment of a trapezoid
• The midsegment of a
trapezoid is parallel
to each base and its
length is one half
the sums of the
lengths of the bases.
• MN║AD, MN║BC
• MN = ½ (AD + BC)
B
M
A
C
N
D
Ex. 3: Finding Midsegment lengths of trapezoids
• LAYER CAKE A baker is
making a cake like the
one at the right. The
top layer has a diameter
of 8 inches and the
bottom layer has a
diameter of 20 inches.
How big should the
middle layer be?
• Use the midsegment
theorem for trapezoids.
• DG = ½(EF + CH)=
½ (8 + 20) = 14”
E
D
C
F
G
D
Parallelogram Properties
http://math.kendallhunt.com/x19430.html
http://www.mathwarehouse.com/geometry/quadrilate
rals/parallelograms/#anglesParallelogram
http://www.youtube.com/watch?v=ioTBllxJ91s
if a quadrilateral is a parallelogram
opposite sides are parallel (DEFINITION)
opposite sides are congruent
opposite angles are congruent
consecutive angles are supplementary
diagonals bisect each other
Using Properties of Parallelograms
• PQRS is a parallelogram. Find the angle
measure.
 m< R
 m< Q
Q
=70 °
70 ° + m < Q = 180 °
70°
P
m< Q = 110 °
R
S
Debrief
What did you learn today?
What will you do to be ready to do your best on
the final exam?