When completing this last blog i will use my previous data to answer these questions:

• What does this make you think about triangles?
• Have you discovered any more patterns?
• Do you think the chart and data helps with the investigation? and do i have anymore questions?

1. when looking at the data that i have collected, it shows me that when the two sides of the right triangle are increased by the same number, the angles increase but are still congruent to eachother. i also know that two triangles can have congruent angles even if they have different side lengths.

2. i have discoverd more patterns when looking at the data that i have collected. i noticed that when side AC stays at a measurement of 9 and side BC decreases in measure by 1, angle A is smaller than angle B. i also noticed that as side BC decreases, angle B increases. when both sides are congruent, the angles are going to be congruent as well. since it is a right triangle, the angles are going tobe more than 30 degrees and less than 90 degrees.

3. i do believe that the charts and data do help with the investigation. that is because i am able to see the side lenths and angles of the triangles. when i have the data i am able to look at it and see if i can find any specific patterns or changes. with out the data or chart i believe this investigation would have been harder.

Some questions that I have are:

• Why in the data, the angles are decimals when the sides are whole numbers??

When looking at the chart below, i found a pattern. When sides AC and BC are the same, the angles A and B are congruent. In the first graph, side AC stays at 9 and the side BC decreases by 1. Angle A decreases by at least 4 degrees while angle B increases by at least 4. When side AC stays at 9, and side BC decreases by an equal amout. When looking at the angles, they are all in the 40 degrees. i think you can predict the angles of triangles when you have the side lengths.

If you know the side lengths of a right triangle, can you pretict what the angles will be? #3

I noticed that when you change a side, it also affects the angle. When all sides are equal, all the angles are equal. It is hard to find angles without one given angle. It would be easier to find the angles by using a protractor. If you increase the sides, the angles increase also. if you decrease the sides, the angles decrease. I haven't found a pattern yet. The sides of the triangles are whole numbers. The angles of the triangles are decimals. The angles don't increase or decrease in a certain order.

If you know the side lengths of a right triangle, can you predict what the angles will be?

.	Side AC:	9	9	9	9	9	9
.	Side BC:	9	8	7	6	5	4
.	Hypotenuse AB:	12	12.042	11.402	10.817	10.296	9.849
.	Angle A:	45	41.63	37.88	33.69	29.05	23.96
.	Angle B:	45	48.37	52.13	56.31	60.95	66.04
.
.	Side AC:	9.5	8.5	7.5	6.5	5.5	4.5
.	Side AB:	9	9	9	9	9	9
.	Hypontenuse BC:	13.086	12.379	11.715	11.102	10.548	10.062
.	Angle :B	46.548	43.363	39.806	35.838	31.43	26.565
.	Angle C:	43.452	46.636	50.194	54.162	58.57	63.435
.
.	Side AC:	8	8	8	8	8	8
.	Side BC:	9	8	7	6	5	4
.	Hypotenuse AB:	12.042	11.314	10.63	10	9.434	8.944
.	Angle A:	48.37	45	41.19	36.87	32.01	26.57
.	Angle B:	41.63	45	48.81	53.13	57.99	63.44

-Chart Taken From Dominique's Page

This shows the relationship between the sides and the angles. One pattern that I noticed is that when you change the size of side AC which is the longer side of the triangle, Angle A's measure decreases, but the measure of Angle B increases. This pattern also works when you change the length of side BC, the shorter side of the triangle. Just as the measurement of Angle A, the size of the hypotenuse decreases.

If you know the side lengths of a right triangle, can you pretict what the angles will be? #2

when looking at the chart above you can see that when the two side lengths are the same, the angles are also the same. since they are both measure 45, you can tell the third angle is 90. looking at the other side lengths that are not the same, you can also see that the angles are different as well. i dont think i would have been able to find those angle measurements when looking at the side lengths.

If you know the side lengths of a right triangle, can you pretict what the angles will be?

Lengths: Angles:
AC = 9 A = 45
BC = 9 B = 45

AC = 6 A = 56.31
BC = 9 B = 33.69

AC = 9 A = 29.05
BC = 5 B = 60.95

i noticed that when i changed one of the side lengths of the triangles, the other side length didn't change. on the website, http://www.shodor.org/interactivate/activities/SquaringTheTriangle/,when i changed the side length AC, length BC stayed the same. i noticed that when i changed the side length AC, angle A increases and Angle B decreases. When i increased side BC angle B increased and angle A decreased.