Friday, September 26, 2014

Chapter 3 Test (Day 36)

As usual, let me give some insight on the test:

1. C' is the same as C, but D' goes up diagonally to the left. This is tricky because the line of reflection is not perfectly vertical.

2. I' goes up diagonally to the right.

3. There are two symmetry lines -- the segment joining the two points and its perpendicular bisector.

4. The angle measures 62 degrees.

5. The angle measures 2x degrees.

6. The reflection image over line AD of ray AB is ray AC. This is tricky because it's been a while since we've seen the Side-Switching Theorem.

7. This is officially the Figure Reflection Theorem -- just make the right vertices correspond.

8. Reflections preserve distance.

9. The orientation is clockwise.

10. The orientation is counterclockwise, because reflections switch orientation.

11. There are three pairs: angles B and C, angles BAD and CAD, angles ADB and CDB.

12. There is one line of symmetry -- the line containing the angle bisector. This follows from the Angle Symmetry Theorem.

13. F' = E follows from the Flip-Flop Theorem. FG = EH is because reflections preserve distance.

14. Proof:
Statements          Reasons
1. MO = MN       1. Given
2. M' = N            2. Given
3. MO = NO       3. Reflections preserve distance
4. MNO is equil. 4. Definition of equilateral

It's possible to add more details, such as O' = O, Transitive Property, etc.

15. The rectangle has two lines of symmetry, one horizontal, one vertical.

16. The isosceles triangle has one line of symmetry, and it's horizontal.

17. The images of the vertices are (1,3), (7,1), and (6,-2).

18. The image is (c, -d).

19. The angle measures 140 degrees.

20. The shortest distance is the perpendicular distance.

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