7.3
The names of the three sides of a right triangle. (Hint: This is on page 405)
What are legs and hypotenuse?
Test the converse of the pythagorean theorem to see if this is a right triangle:
Leg 1 - 6 feet
Leg 2 - 8 feet
Hypotenuse - 10 feet
This is a right triangle.
How can you find the distance between two points on a coordinate plane?
1. Use the points to draw a right triangle. 2. Determine the lengths of the legs by counting. 3. Use the pythagorean theorem to find the hypotenuse.
If it is a vertical or horizontal line, you can just count the units on the plane.
Pythagorean Theorem
What is a2+b2=c2?
Solve for x:
102 + x = 234
x = 132
Use the following information to find the length of the hypotenuse (round to the nearest tenth):
a = 3 inches
b = 5 inches
c = ?
What is 5.8 inches?
If the sum of the squares of the legs do not equal the square of the hypotenuse, is the triangle a right triangle?
(a2+b2 is not equal to c2)
No it is not a right triangle.
Find the distance between (-3, -4) and (1, 2). Round to the nearest tenth.
The distance is 7.2 units
Converse of the pythagorean theorem
If a2+b2=c2, then the triangle is a right triangle.
Exterior angle of a triangle
Formed by one side of the triangle and the extension of the adjacent side.
What is the missing side length?
a = 5 feet
b = ?
c = 13 feet
What is 12 feet?
If a triangle has side lengths of 14 cm, 18 cm, and 20 cm, is it a right triangle?
No it is not a right triangle
Find the distance between the points (3, 0) and (7, -5). Round to the nearest tenth.
The distance is roughly 6.4 units.
Perpendicular Lines
Two lines that intersect to form a 90 degree angle (right angle)
Sum of the interior angles of a triangle
180 degrees
Find the hypotenuse of a right triangle when one leg is 12 cm and the other leg is 9 cm.
What is 15 cm?
If a triangle has side lengths of 10 in, 24 in, and 26 in, is it a right triangle?
Yes it is a right triangle.
Find the distance between (0, 0) and (-4, -3).
What is 5 units.
Right Triangle
A triangle with one 90 degree angle.
Alternate Interior Angles
Angles that lie on opposite sides of a transversal and inside of the parallel lines.
Find the missing leg when the other leg is 12 in and the hypotenuse is 20.8 in. (Round to the nearest whole number.)
What is 17 in?
Is a triangle with side lengths of 1 mm, 2 mm, and 3 mm a right triangle?
Find the distance between (2, 1) and (9, 1)
What is 7 units.
What is the hypotenuse
The longest side of a right triangle.
The side opposite the right angle.
What is Ms H's favorite number?
23