4.2+Analyzing+Triangles

²2/11/08 AE

Problem 4.2 Analyzing Triangles

A)Trianlge ABP is half of an equilateral triangle. They are symmetrical (the exact same), they both have a right angle and there other two angles are the same.
 * A) How does triangle ABP compare with triangle ACP?**


 * B)Find the measure of each angle in triangle ABP. Explain how you found each angle.**

B)Well I know that angle P is 90° because it is a right angle. I also know that each triangle's angles add up to 180°, so 180º- 90º = 90º. So there are 90º left over and angle B is twice the size of angle A so 60º for angle B, and 30º for angle A.


 * C)Find the length of each side of triangle ABP. Explain how you found each length.**

C)Since the ORIGINAL triangle was an equilateral triangle, all the sides are the same. Since the triangle was cut in half that means that one of the sides stay the same, while one is cut in half and the other one you have to find the Pythagoreas Therom. The hypotanuse C) 2, I know this because since the triangle was cut in two, the hypotanuse will stay the same. Then, A is 1 because it use to be two until it the triangle was cut in half. To find out B we have to 'reverse' the Pythagoreas Therom. Instead of using a²+b²=c² we have to use b² = c²-a² because we are trying to find B.

So, 1²+ b²=2² 1+ b² = 4 b² =3 b = squareroot of 3.


 * D)Two line segments that meet at right angles are called perpendicular line segments. Find a pair of perpendicular line segments in the drawing above.**

D)


 * E)What relationships do you abserve among the side lengths of triangle ABP?**

E)You can use the Pythagoras Theorey because it's a right triangle. It's a 30-60-90 triangle which is half of an equilateral triangle.


 * E)Are these relationships true for triangle APC?**

E)Yes because it's the same triangle put together to make an equilateral triangle.


 * Problem 4.2 Follow-Up

1)A right triangle with 60° angle is sometimes called a 30-60-90 triangle. This 30-60-90 triangle has a hypotanuse of length 6. What are the lengths of the other two sides?**

1)The side lengths are 3, 6, and 5.196. The way that I know these answers is because this was first an equilateral triangle, and then it was cut in half so the hypotanuse is still the same, and the base is divided by 2 so 6/2 = 3. So that takes care of 6 and 3. Now to find the straight side you have to do the base times the squareroot of 3. Which is 5.196.


 * 2a)How do the 2 triangles compare?**

2a)They are both isosceles and are both right triangles, they are also the same size.


 * 2b)What are the angles?**

2b)The angles are 90° for C, B&D are 45° this is because all the angles must add up to 180° and the triangle is isosceles.


 * 2c)What is the length of the diagnol?**

2c)The length of the diagnol is the squareroot of 2 = 1.402. I know this because 1²+1²=squareroot of 2.

2d)If the side lengths of the squares were 5 then...

2d)The angles would stay the same, so they'd still be; C-90°, and B and D would be 45°.

2d)The lengths of the diagnol would change to 5²+5²= the squareroot of 50. This is because the side lengths are 5.