Pythagorean
Theorem
a2 + b2 = c2
Pythagorean
Triples
A set of three positive integers
a, b, and c that satisfy the
equation a2 + b2 = c2
Common Triples:
3, 4, 5
8, 15, 17
Converse of the
Pythagorean
Theorem
1.) Identify the unknown as a leg or
hypotenuse and find the length.
In a right triangle, the sum
of the squares of the measures
of the legs equals the square of
the measure of the hypotenuse.
2.)
5, 12, 13
7, 24, 25
If the sum of the squares of the measures of two sides of a triangle
equals the square of the measures of the longest side, then the triangle
is a right triangle.
Methods for Classifying Triangles by Angles Using its Side Lengths
Theorem 7.2
A
C
Theorem 7.3
A
B
C
Theorem 7.4
A
B
C
B
If c2
a2 + b2, then
If c2
a2 + b2, then
If c2
a2 + b2, then
m∠C
90˚ and ΔABC
m∠C
90˚ and ΔABC
m∠C
90˚ and ΔABC
is a ________________Δ.
is a ________________Δ.
is a ________________Δ.
Decide whether the numbers can represent the side lengths of a triangle. If they
can classify the triangle as acute, right or obtuse.
4.) 4, 10, 12
5.)
13 , 6, 7
Word Problems:
Door A 6 foot board rests under a doorknob and the base of the board is 5 feet away from the bottom
of the door. Approximately how high above the ground is the doorknob?
In real-world applications, it is
usually appropriate to use a
calculator to approximate the
square root of a number. Round
your answer to the nearest tenth.
Ladder You are tasked with washing the outdoor windows of your home. Your 12-ft. ladder reaches a
height of 9 feet allowing you to reach all of the window. How far is the base of the ladder from the
home? (Round your answer to the nearest tenth.)
Altitude – a perpendicular segment from a vertex to the opposite side
*In isosceles and equilateral triangles, the ____________________will
____________________ the base.
Find the length of the altitude in this triangle.
-Find the area of an isosceles triangle
,
note that ___________ ALWAYS
Find the area of the isosceles triangle with side lengths 16 meters, 17 meters, and 17
meters.
Step 1 Draw a sketch.
Step 2 Use the Pythagorean Theorem to find the height of the triangle.
Step 3 Find the area.
Practice: Find the area of the triangle. Round intermediate values to the nearest tenth.
Find the area and perimeter of each triangle. Keep exact values.
1.)
2.)
Area = _______
Area = _______
Perimeter=______
Perimeter=______
Classify each triangle as acute, obtuse or right. Do not go by the look of the
triangle, but rather do the “math.” Show your work.
3.)
4).
51
16
24
11
45
14
The numbers represent the lengths of the sides of a triangle (or do they?). Classify
each triangle as acute, obtuse or right. Show your work.
5.) 3, 6, 7
6.) 4, 8, 12
SOL Questions:
8.) Mr. Ammons is constructing a walkway through his rectangular
garden. The walkway runs diagonally as shown in the diagram.
Which is closest to the length of the walkway?
A 18.7 ft
B 28.3 ft
C 30.0 ft
D 39.0 ft
9.) What is the length of ̅̅̅̅
𝑆𝑈?
A 2√7 cm
B 7 cm
C 4√7 cm
D 20 cm
7.) 9, 12, 15