Pythagorean Theorem
Reference Triangles
Distance
Circles
100
State the Pythagorean Theorem and draw a picture where it could apply.
a2+b2=c2
100
If the hypotenuse of a right triangle has length 2y and the shorter leg has length y, which reference triangle would be similar to this triangle? What is the length of the longer leg?
30-60-90
y(sqrt3)
100
Find the distance between (3, 7) and (-1, 11).
4(sqrt2)
100
Find the center of the circle and its radius from the equation (x+5)2+(y-1)2=25.
center is (-5, 1) radius is 5
200
Is a triangle with side lengths of 11, 13, and 17 a right triangle?
No
200
In an isosceles right triangle, if one leg has length w, what is the length of the hypotenuse?
w(sqrt2)
200
Find the radius of a circle with a center at (-5, 11) and a point on the circle (-8, 17).
3(sqrt5)
200
Write the equation of a circle with center (1, 7) and radius 7.
(x-1)2+(y-7)2=49
300
What is the length of the hypotenuse of a right triangle with legs of length 160 feet and 300 feet?
340 feet
300
If the area of a square is 289 cm2, what is the length of the diagonal of the square?
17(sqrt2)
300
Points A(-1, 3), B(-4,3), and C(-1,0) lie in the standard coordinate plane and are 3 vertices of square ABCD. What is the length, in coordinate units, of BD?
3(sqrt2)
300
Write the equation of a circle with center (-4, 3) and radius 2.
(x+4)2+(y-3)2=4
400
The width of a rectangle is 21 feet and the length is 28 feet. What is the length of the diagonal of the rectangle, in feet?
35 feet
400
Find the exact circumference of a circle inscribed in a square with a diagonal of 4(sqrt2).
4pi
400
A is at (-1, 3) and B is at (-4, 11). Draw AB as the hypotenuse of a right triangle and find length AB.
AB is sqrt73
400
Find the center of the circle and its radius from the equation (x+11)2+(y+2)2=10.
center (-11, -2) radius (sqrt10)
500
Two students are standing together in the mall. One student walks south at 3 feet per second and the other walks east at 4 feet per second. How far apart, in feet, are the students after 3 seconds?
15 feet
500
What is the exact length of the hypotenuse of a 30-60-90 right triangle with a longer leg of 12m?
8(sqrt3)
500
Triangle ABC has vertices, A (3,5), B (-1, 10), and C (-5, 15). Is ABC scalene, isosceles, or equilateral?
Isosceles
500
If you plot the equation x2+(y-3)2=9 as a circle on a standard xy-graph, what is the area of the circle's region that will lie in Quadrant 1?
4.5pi