Download - 1.11 Day 3
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Please grab your calculators on your way into the room and start on the Bell Ringer.
•Find a pair or group of angles that have an invariant sum of 180 degrees.
•If you move point D along line C, will the area of triangle DEF change.
Bell Ringer
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What is the sum of the measures of the angles of a 20-sided polygon? 9-sided polygon? 17-sided polygon?
20 Sided – 3240 degrees
9 sided – 1260 degrees
17 sided – 2700 degrees
What is the measure of each angle in a 9 sided polygon?
1260/9 = 140 degrees
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What is the area of the shaded region?
Area of square – area of circle = shaded region
L X W
8 x 8 – ( (3.14) x 42 )
64 – 50.24 = 13.76
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What relationship do you see between the lengths of CD and DA, as well as AE and EB?
CD = DA (because D is the midpoint of segment AC)
AE = EB (because E is the midpoint of segment AB)
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Compare the lengths of segment DE and segment CB as you drag one of the vertices.
As segment CB gets larger, so does segment DE.
DE/CB = ½
2DE = CB or 1/2CB = DE
Segment DE
Segment CB
DE/CB
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Midline Conjecture
A segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half its length.
What invariants did you find in triangle ABC as you moved one of the vertices?
AD/AC
AE/AB
DE/CB
Area of triangle AED/Area of triangle ABC
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What is the length of segment AD, EC and BC?
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What is the length of segment AD, DB, EC, and DE
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Given that DE is a midline:
If DE = 10, find the length of CB.
If CB = 10, find the length of DE.
If AC = 14, find EC.
If AD = x + 5 and DB = 20, find the value of x and find the lengths of AD and AB.
If DE = 6 and CB = 3x – 4, find the value of x.
f) If the height of the triangle is 7cm and the base of the triangle is 6 cm. What is the area of the triangle?
ED
B
A
C