Honors Geometry_8.3_Jan 30
8.3 Warm−up
1) The perimeter of a rhombus is 40 cm, and one diagonal is 12 cm long.
How long is the other diagonal?
10
8.3
Converse of the
Pythagorean Theorem
6
6
2) Solve for x.
I can...use the converse of the Pythagorean
Theorem to EXPLAIN why a given triangle is
a right triangle, obtuse triangle, or an acute
triangle when given the measures of all 3
sides. [G.SRT.C.8]
x
x= 28
15
12
15
10
Thm 8.3 - Converse of the Pythagorean Theorem
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.
We can use this to determine whether or not the triangle is a right triangle!
Pythagorean Triples
Pythagorean Triple
A "_______________________"
is a set of three positive integers,
a, b, and c that fits the rule:
c2 = a2 + b2
The smallest Pythagorean Triple is 3, 4, 5.
In ∆ABC,
c
a
2
2
Let's check it:
2
if c = a + b ,
then ∆ABC is a right triangle.
b
Some Common Right ∆ Lengths/ Pythagorean Triples:
1
Honors Geometry_8.3_Jan 30
Theorem 8.4
C
Remember c is always the longest side
If c < a + b , the m∠C < 90°,
and ∆ABC is acute
2
2
2
a
b
B
Theorem 8.5
a
If c > a + b , the m∠C > 90°,
and ∆ABC is obtuse
2
2
2
A
c
C
Tell whether the ∆ with sides of the given lengths is acute, right, or
obtuse.
1.
4, 4√3, 8
2.
2
64
2
4 + (4√3)
16 + 48
2
2
Acute
2
2
2
Right
2
2
2
Obtuse
A
3. 20, 21, 29
4. 2√3, 3√2, 6
29, 32, 24
29
8
2
b
c
B
2
c < a +b
c = a +b
c > a +b
2
841
2
20 + 21
2
400 + 441
841 = 841 right
6
2
36
2
(2√3) + (3√2)
2
12 + 18
36 > 30
obtuse
64 = 64 right
2
Honors Geometry_8.3_Jan 30
p 297
8.3 Assignment:
WE 1-9 odd, 10 -14 all, 16
Solutions
3