PT INEQUALITY
Pythagorean Inequality Theorem for obtuse triangles.
a2+b2 < c2
Find the midpoint between points A and B.
A(-3, 1) and B(1,-4)
M(-1,-3/2)
A right triangle has legs measuring 6 and y mm, and a hypotenuse measuring square root of 85 mm. Find y.
7 mm
Is this equivalent to the Distance Formula?
(x2-x1)2+(y2-y1)2=c2
Yes!
How many letters are in the longest side of a right triangle?
10 letters
Pythagorean Inequality Theorem for acute triangles.
a2 + b2 > c2
Point A(-3.5, -5.5) has a midpoint M(-1, 7) between A and Point B. Find B.
B(1.5, 19.5)
Find the diagonal of the rectangular prism with the following measurements.
Length: 10 cm
Width: 6 cm
Height: 6 cm
Round to the nearest tenth if needed.
13.1 cm
Find the distance between (-8,-7) and (2,13) in simplest radical form.
10 root 5
True or False?
The midpoint between (-5.1, -2) and (1.4, 1.7) is (-1.85, -0.15).
TRUE!
Define and name the theorem for right triangles.
Pythagorean Theorem; a2+b2=c2
Find endpoint B.
A(-5, 5) and M(2,-5)
B(9, -15)
A repairman leans the top of an 8 ft ladder against the top of a stone wall. The base of the ladder is 5.5 ft from the wall. Is the wall taller than the ladder...or vice versa? By how much?
wall is about 5.8 ft; ladder is taller by 2.2 feet
Plot the points (0,-6) and (3,7) and find the distance. Round to the nearest tenth if needed.
13.3 units
4 root 3 squared.
48
The lengths of a triangle are: 13, 17, 15. What kind of triangle is this?
acute
J-----------K----------L
K is the midpoint between J and L.
If JK=5x-2 and KL=9x-30, what is the length of JL?
66 units
Find the diagonal of a rectangular prism with the following measurements.
Length: 5 in.
Width: 5 in.
Height: 5 in.
Round to the nearest tenth if necessary.
8.7 inches
Find the distance between (-4,9) and (-2,-1) in simplest radical form.
2 root 26 units
Which of the following could not represent the sides of a right triangle?
A: {42, 56, 70}
B: {3, 4, 5}
C: {39, 52, 64}
C
Define acute and obtuse triangles.
Acute triangle = all 3 angles are < 90 degrees;
Obtuse triangle = 1 angle is > 90 degrees and 2 angles are acute
Find the point that is 1/4 of the way
from (2, 4) to (10, 8).
(4, 5)
A triangle has sides of 15, 20, and 25 meters. Is this a right triangle? Explain why and support your answer with the correct theorem.
Yes; 152+202=252
Converse of the Pythagorean Theorem
Can you use the Pythagorean Theorem to find the distance between (x1, y1) and (x2, y2)? Find the answer/ explain why it's not possible.
YES!
sq root of [(x2-x1)2+(y2-y1)2]
Simplify the square root of 2400
20 root 6