3.4
Is It A Right Triangle?
Pg. 13
Pythagorean Theorem Converse and Distance
3.4 – Is It A Right Triangle?_______________
Pythagorean Theorem Converse and Distance
In lesson 3.3, you learned how to use the
Pythagorean Theorem. Today you are
going to use this information to find the
length between two points on a graph. You
are also going to determine if the triangle is
acute, right, or obtuse.
3.24 – DISTANCE
Use the Pythagorean theorem to find the
following.
A
2
l h
2
72 + 32 = d2
49 + 9 = d2
58 = d2
58  d
2
7
d
3 B
b. A(-6, 2)and B(-2, -3)
2
l h
42
52 =
2
2
A
d2
+
16 + 25 = d2
41 = d2
41  d
d
5
4
B
c. A(-1, 2)and B(3, 4)
2
l h
22
42 =
2
2
d2
+
4 + 16 = d2
20 = d2
2 5d
4
2
A
x
B
Distance Formula:
x y d
2
2
2
y2 – y1
x2 – x1
3.25 – DISTANCE FORMULA
Find the distance between the two points.
Simplify your square roots.
a.
A(2, 4)and B(8, 19)
x y d
2
2
2
62 + 152 = d2
36 + 225 = d2
261 = d2
d = 3 29
b.
A(-2, 3)and B(-8, 6)
x y d
2
2
2
62 + 32 = d2
36 + 9 = d2
45 = d2
d= 3 5
c.
A(-5, 2)and B(-2, -7)
x y d
2
2
2
32 + 92 = d2
9 + 81 = d2
90 = d2
d = 3 10
3.26 – WHAT'S THE PATTERN?
Use the tools you have developed to find
the lengths of the missing sides of the
triangles below. If you know a shortcut,
share it with your team. Look for any
patterns in the triangles as you solve. Are
any triangles similar and multiples of
others? Keep answers in exact form.
5
10
5000
x  3 4
2
2
2
x 6 8
2
2
2
x 2  30002  40002
12
132  x 2  5 2
24
262  x 2  102
120
130 2  x 2  502
3.27 – PYTHAGOREAN TRIPLES
5
4
3
13
12
5
3.28 – EXTRA PRACTICE
Find the area of the shapes using
Pythagorean triples to help find the
missing sides.
3
4
8
A  triangle  rectangle
A
1
bh
2
 bh
1
A
 4   3    8 3
2
 24 
A
6
30un
2
8
1
A  bh
2
1
A   36   8 
2
A  144un
2
30
5 20
30
20
5
A = 100un2
Acute
Triangle
Right Triangle
b
c
b
c
Obtuse
Triangle
c
b
a
a
a
c a b c  a b c a b
2
2
2
2
2
2
2
2
2
3.29 – TRIANGLE CLASSIFICATION
For each set of numbers, determine if the
triangle is acute, right, or obtuse. SHOW
WORK!
a.
8, 15, 17
17  8  15
289  64  225
289  289
2
2
2
ACUTE, RIGHT, or OBTUSE
b.
3, 5, 7
7  3 5
49  9  25
49  34
2
2
2
ACUTE, RIGHT, or OBTUSE
c.
8, 10, 12
12  8  10
144  64  100
144  164
2
2
2
ACUTE, RIGHT, or OBTUSE
d.


2
89  5  8
89  25  64
89  89
2
2
ACUTE, RIGHT, or OBTUSE
e.

8 5  3 7
2
2

2
64  25  63
64  88
ACUTE, RIGHT, or OBTUSE
f.

12  2 10
2

2
9
144  40  81
144  121
ACUTE, RIGHT, or OBTUSE
2