Download 1.10 Pythag Day #2

Name:
9/22/14 or 9/23/14
Geometry (2)
Pilch
More on Radicals and Pythagorean Theorem – NOTES AND HW #7
The Converse of the Pythagorean Theorem
If the square of ________________________of a triangle is equal to the
_______________________________, then the triangle is a right
triangle.
Example 1: Can 3, 4 and 5 be the sides of a right triangle?
Example 2: Can 3, 5 and 7 be the sides of a right triangle?
Example 3: A bit more on simplifying radicals….
(a)
2 7 + 5 5 – 2 5 + 6 7 – 50 + 8
(c)
2 3•4 6
18 + 32 + 75
(b)
(d)
(2 3)
2
HOMEWORK #7
1. Which triples can be sides of right triangles?
If it is a right triangle, tell which length is the hypotenuse.
A. 5, 12 and 13
B. 2, 4 and 6
Using the Pythagorean Theorem:
2.
3.
C. 2,
2 and 2
4.
5.
Add or subtract, leaving your answer in the simplest possible form:
(a)
6A).
18 + 8
62 = _____
B.
(b)
( 6)
____
7. Find the midpoint of AB
8. XY =
X
2
= ______
C.
3 + 24 + 54
2x • 5x = _______
A (-1, 3) B ( 3, 1)
D. 2 2 • 5 8 = _______
Perhaps draw a picture
1
x + 5 , YZ = 4x and XZ = 32. Find x, XY and YZ.
2
Y
Z
x = _________ XY = _________ YZ = _________
9. M is the midpoint of AB. AM =
A
M
5
x + 2 and BM = 15. Find x.
7
B
Relationship: ___________________________ because _____________________________
X = ________
10. Find the perimeter (length around the outside) of the rectangle shown.
11. Which triples can be sides of right triangles? If it is a right triangle, tell which length is the
hypotenuse.
A.
6, 8 and 10
B.
5, 6 and 7
C.
2, 2 3 and 4
12. A baseball diamond is a square with sides 90 feet long. What is the shortest distance (to
the nearest tenth of a foot) between first base and third base?
13.