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

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

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

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)

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

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

What is the length of segment AD, EC and BC?

What is the length of segment AD, DB, EC, and DE

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