## Monday, March 14, 2011

### Chapter 5 Project: How to Do Determining the Number of Triangles in the Ambuguous case (SSA): A Contruction Exploration

Exploration 1:

1. First, I drew a line that is over 6 cm and drew a point on that line and labeled it A.
2. Then, I constructed a 120 degree angle.
3. Afterwards, i made a 7 cm arch using a compass. Then the arch touched the 120 degree angle line, so I label it point C. *Note: in my Exploration 1, 1 the 7cm line is suppose to touch point B but it accidently got cut off.
4. I did the same for the other lengths using 5 and 6 cm.

Questions:

1. For 1, I discovered that there was one triangle that could have been made and for 2 and 3, i learned that zero triangles could be made.
3. The rule: BC > AB to make a triangle.

1. First, I drew a 30 degree angle with a protractor.
2. Then, i constructed a perpendicular bisector through point C and measured my height (3.5 cm).
3. Next, i copied a 30 degree angle and drew ray AC and AB.
4. Afterwards, I constructed a perpendicular bisector from AC to ray AB to form a right triangle.
5. I then found a value less than 3.5 cm (2 cm) and drew an arch from point C to see if a triangle could be formed. A triangle couldn't be formed.
6. I repeated steps 3-4 but for the next two triangles, I used a segment equal to the height of my triangle (3.5 cm) and a segment where BC>AC>h (7.3 cm).

Questions-

1. I discovered that i could make zero triangles in 6a, 1 right triangle in 6b, and 2 triangles in 6 c.
2. Rule: Triangles can only be made if its length is equal or greater than its height.

Exploration 3:

1. First, i drew a 30 degree angle with a protractor.
2. Then, I drew a 7 cm and 6 cm segment.
3. Next, I drew a line through the page and made a point and labeled it A.
4. I constructed a 30 degree angle with the line segment of 7 cm.
5. After that, I connected the points and labeled it Line segment AC= 7 cm.
6. Then, I used a 6 cm segment to draw arches on line AB-which should make two archs.
7. I connected these arches to point C, which then formed 2 triangles.
8. Finally, i created a perpendicular bisector through point C and measured the height.

The rule I got was AC>B>h

Questions:

1. SinA is the same as SinC
2. If BC is < or = AB, it can cause a right triangle or obtuse triangle to form.
3. BC = AB makes zero triangles
BC > AB makes one triangle
BC < AB makes zero triangles
BC < h makes zero triangles
BC = h makes one triangle
BC > AC > h makes two triangles
AC > B > makes two triangles