Pick up your calculators on your way into the room.

Find the numerical invariance in the table below.

Q T

1/8 ½

4 16

8 32

100 400

Constant Numerical Invariant

Position of pointIntersection of linesLengths of segmentsMeasure of anglesSums of ratios

What can be invariant?

Which measures seem invariant in triangle DEF as D moves along line CD?

The area of triangle DEFThe sum of the measures of angles D, E, and F

How do you find the area of a triangle?

Area of a triangle = ½ base X height

Example 1

A = ½ (7X4)

A= ½(28)

A= 14 units2

Example 2A= ½ (5X12)

A = ½ (60)

A = 30 units2

What is the height of triangle ABC if the area is 24 in2 and the base is 12 in ?

A = ½ (bXh)

24 = ½ (12Xh)

24 = 6h

4 = h

What is the base of triangle LMN if the area is 14 cm2 and the height is 2cm?

14 = ½(bx2)

a. Measure of angle CDE = Measure of angle DEF

b. Measure of angle CDE + EDF + EFD = 180 degrees

c. Measure of angle EFD is less than measure of angle AED

and

Measure of angle FED is less than measure of angle BFD

Write your summary and turn in your Cornell Notes.