course Mth 151

6/22 12 a.m.

Question: `q001. . There are five questions in this set.

Draw four points in a square pattern (i.e., if the points were properly connected, they should form a square). From each of

the points, draw a straight line to each of the other points. How many lines did you draw?

Your solution:

There are four points so you would be drawing a line to the other 3 so 4*3=12. You draw a total of 12 lines.

*********************************************

Question: `q002. How many triangles are there in the figure you drew?

Your solution:

You have 4 large triangles and 4 smaller triangles for a total of 8 triangles

*********************************************

Question: `q003. The lines you drew should form a square with its two diagonals. Label the corners of the square A, B, C and

D, going in order around the square, and label the center where the diagonals cross E. Now list all possible combinations of

3 of the letters A, B, C, D, E (note: combinations don't care about order, so A D E is the same as D A E or E A D or any

other combination of these same three letters, so list each possible combination only once. That is, if you list for example

ADE you won't list DAE).

Your solution:

You would have 10 combinations they are B,D,C: B,A,C: A,B,D: A,D,C: B,E,C: B,E,D: A,E,C: A,B,E: A,E,D: C,D,E

*********************************************

Question: `q004. Of the 10 combinations ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, CDE, which form triangles on your

figure?

Your solution:

A,B,D: A,C,D: A,B,C: B,D,C: A,B,E: B,E,D: D,E,C: C,E,A: A,E,C: A,D,E

*********************************************

Question: `q005. Sketch the same figure as before, but without the line segment from A to B. Now how may triangles are there?

Your solution:

This leaves us the five triangles ACD, ADE, BCE, BCE and CDE.