Pythagorean Theorem

Question 1

What is (Theorem 8 - 2) the Pythagorean Theorem?

Answer 1

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.

a^2 + b^2 = c^2

Question 2

What is Theorem 8 - 3 (Converse of the Pythagorean Theorem)?

Answer 2

If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

Question 3

What are the Pythagorean Triplets?

Answer 3

3, 4, 5

and

5, 12, 13

and

8, 15, 17

and

7, 24, 25

Question 4

What is Theorem 8 - 4?

(Acute Triangles)

Answer 4

(in a^2 + b^2 = c^2)

if c^2 < a^2 + b^2,

then m<c>acute</c>

Question 5

What is Theorem 8 - 5?

(Obtuse Triangles)

Answer 5

(in a^2 + b^2 = c^2)

If c^2 > a^2 + b^2,

then m<c>90 and Triangle ABC is <strong>obtuse</strong></c>

Question 6

Is the triangle acute, right or obtuse?

a. 20, 21, 29
b. 20, 21, 30
c. √3, √4, √5
d. 8, 5, 2

Answer 6

a. 841 = 400 + 441 → right Triangle
b. 900 < 400 + 441 → acute Triangle
c. ²(√5) < ²(√4) + ²(√3) → acute Triangle
d. Not a Triangle, bc 2 is < the diff which is 3 even though it is < than the sum which is 13. Check before assuming its a triangle.

Question 7

What is the difference btwn Thm 8 - 3/4/5?

Answer 7