Show:
Simplifying Radicals and
Rationalizing Denominators
Pythagorean Theorem
Distance / Midpoint
Classifying Triangles
Special Right Triangles
100

Simplify √8

What is 2√2

100

Write the Pythagorean Theorem

What is a^2 + b^2 = c^2

100

In common English, describe 

a) What the distance between two points is and 

b) What the midpoint between two points is.

What is:

a) how far apart two points are

b) The halfway point between two points.

100

If c^2 < a^2 + b^2, this type of triangle is formed.

What is acute?

100

If one leg of a 45-45-90 triangle is x, these are the lengths of the other two sides.

What is:

Other leg: x

Hypotenuse: x√2?

200

Simplify √24

What is 2√6?

200
In order for the pythagorean theorem to work, a triangle has to be this kind of triangle.

What is a right triangle?

200

Find the midpoint between (0,0) and (6,10)

What is (3,5)?

200

This type of triangle has 2 congruent sides.

What is isosceles?

200

If the shorter leg of a 30-60-90 triangle is x, these are the lengths of the other two sides.

What is:

Longer leg: x√3

Hypotenuse: 2x?

300

Simplify √120

What is 2√30

300
If two legs of a right triangle are 3 and 4, this is the length of the hypotenuse.

What is 5?

300

Find the distance between the points (3,11) and (-1,10).

What is √17?

300

DAILY DOUBLE

The sides of a triangle are 3.1, 4.7, and 5.5. Classify the triangle as acute, right, or obtuse.

What is acute?

300

A 45-45-90 triangle has a leg with length 8. This is the length of the hypotenuse.

What is 8√2?

400

Rationalize the denominator of 6/√3 and fully simplify the resulting fraction.

What is 2√3?

400

If the two legs of a right triangle are 12 and 15, this is the length of the hypotenuse (Must correctly simplify for credit).

What is 3√41?

400

Find the midpoint of the segment created between the points (2,15) and (11, 27).

What is (6.5, 21)?

400

a=4, b=6, and c=7. Classify the triangle as acute, obtuse, or right. Then, Classify the triangle as isosceles, equilateral, or scalene.

What is acute and scalene?

400

The hypotenuse of a 45-45-90 triangle has length 12. This is the length of each leg.

What is 6√2

500

Rationalize the denominator of (2√5)/√8 and fully simplify the resulting fraction.

What is (√10)/2?

500

If one leg of a right triangle is 7 and the hypotenuse of the triangle is √97, find the other leg of the triangle. Answer must be simplified to earn credit.

What is 4√3

500

Find the distance between the points (-27,41) and (11,-50). If you simplify you will get double points

What is √9725 = 5√389

500

Point A(0,0)

Point B(2,0)

Point C(1,√3)

Find the length of each leg of the triangle, then classify it based on its angles and side lengths.

What is an acute, equilateral triangle.

500

The longer leg of a 30-60-90 triangle is 15. This is the length of the hypotenuse.

Hint: Find the short leg first.

What is 10√3?