1. Pick up your calculators on your way into the room.
1.11 Numerical Invariance
Pick up your calculators on your way into the room.
Find the numerical invariance in the table below. Q T
1/8 4 16 8 32
100
400

2. Constant
Numerical Invariant
Position of point
Intersection of lines
Lengths of segments
Measure of angles
Sums of ratios
What can be invariant?

3. Which measures seem invariant in triangle DEF as D moves along line CD?
The area of triangle DEF
The sum of the measures of angles D, E, and F

4. How do you find the area of a triangle?
Area of a triangle = ½ base X height
A = ½ (7X4)
A= ½(28)
A= 14 units2
Example 1
Example 2
A= ½ (5X12)
A = ½ (60)
A = 30 units2

5. 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)

6. Measure of angle CDE = Measure of angle DEF
Measure of angle CDE + EDF + EFD = 180 degrees
Measure of angle EFD is less than measure of angle AED
and
Measure of angle FED is less than measure of angle BFD

7. Homework
Write your summary and turn in your Cornell Notes.