1. 8-1, 1-8 Pythagorean Theorem, Distance Formula, Midpoint Formula
Objectives
Apply the Pythagorean Theorem
Determine whether a triangle is acute, right, or obtuse
Apply the distance formula
Apply the midpoint formula

2. Right Triangles A right triangle is a triangle with a right angle
ypotenuse
hypotenuse
leg
egs
leg
A right triangle is a triangle with a right angle

3. Pythagorean Theorem (leg1)2 + (leg2)2 = hypotenuse2
True only for right triangles

4. Pythagorean Theorem Example2
Leg1 = ? 6
Pythagorean Theorem
22 + X2 = 62
X2 = 62 – 22
X2 = 36 – 4 = 32
X = 32
X ≅ 5.7

5. Determining Acute, Right, or Obtuse for Triangles
Let a, b, c be the lengths of the sides of a triangle, where c is the longest
Acute: c2 < a2 + b2
Right: c2 = a2 + b2
Obtuse: c2 > a2 + b2
A triangle’s sides measure 3, 4, 6
62 ?
36 > = 25
Obtuse

6. Distance on number line-3 -1 -2 1 -8 2 -7 -5 -6 -4
Find AB (distance between A and B)
AB = | -8 – (-5) | = | -3 | = 3

7. Distance in the coordinate planey x
C(2, 3)
1) On graph paper, plot A(-3, 1) and C(2, 3).
A(-3, 1)
2) Draw a horizontal segment from A
and a vertical segment from C.
B(2, 1)
3) Label the intersection B and find
the coordinates of B.
QUESTIONS:
What is the horizontal distance between A and B?
(2 – -3) = 5
What is the vertical distance between B and C?
(3 – 1) = 2
What kind of triangle is ΔABC?
right triangle
If AB and BC are known, what theorem can be used to find AC?
Pythagorean Theorem
What is the measure of AC?
29 ≈ 5.4

8. Distance formula in the coordinate planey x
A(x1, y1)
B(x2, y2) d
then d =

9. Midpoint on a number line4 6 6
M = ?
The location of the midpoint is the average of the endpoints
M =
M = 5

10. Midpoint on the coordinate plane
Graph A(1, 1) and B(7, 9) y x 10 -1 2 4 6 8 -2 3 7 1 5 9
Draw AB
B(7, 9)
Find the midpoint of AB. C
C(4, 5)
A(1, 1)
C = (4, 5)