Pythagorean Theorem and Similar Right Triangles

Geometrical Concepts

100

What are the sides of the triangle next to the right angle?

Legs

150

What is the side of the triangle across from the right angle? (*Side c)

Hypotenuse

200

What is the formula for the Pythagorean Theorem?

What is a²+b²=c²

250

What is the name of the guy who is given credit for discovering the theorem we have been learning about?

Pythagoras

300

What is the only type of triangle that works with the Pythagorean Theorem. (Or a triangle with an angle measuring 90 degrees)

Right Triangle

Pythagorean Theorem

100

When one leg=3 and the other leg=4 then the hypotenuse=?

What is 5

150

When one leg=6 and the other leg=7 then the hypotenuse=?

What is the square root of 85?

200

When one leg=15 and the other leg=22 then the hypotenuse=?

What is the square root of 709?

250

When one leg=7 and the hypotenuse=25 then the other leg=?

What is 24?

300

When one leg=21 and the hypotenuse=35 then the other leg=?

What is 28?

Notation and Process

100

Considering that a²+b²=c² on a right triangle, letters "a" and "b" are used to represent which part of a right triangle?

Leg

150

Considering that a²+b²=c² on a right triangle, the letter in the formula that stands for the length of the hypotenuse of a right triangle

What is "c"?

200

What do we call multiplying a number by itself?

squaring a number

250

The side that always has the longest length in a right triangle

What is the hypotenuse?

300

The operation we used to "cancel" a number squared.

What is taking the square root?

Relationships within Right Triangles

100

Triangles that are a result of a dilation.

What are Similar Triangles?

150

Tracing an altitude (height) to the hypotenuse forms.

Three similar right triangles.

200

This statement denotes that congruent angles and proportional sides correspond to each other. 

 

Similarity statement (example, ΔEGF ~ ΔFGH)

250

The number f in the proportion b:f=f:s.

What is the geometric mean?

300

Find the geometric mean of 4 and 49.

What is 14?

Apply any Theorem

100

Pythagorean triples are positive integers that make a²+b²=c² true. If a and b are 8 and 15, respectively, what is the value of c?

What is 17?

150

Pythagorean triples are positive integers that make a²+b²=c² true. If a and c are 9 and 41, respectively, what is the value of b?

What is 40?

200

An airplane lands at an airport 60 miles east and 25 miles north of where it took off. How far are the two airports?

What is 65mi?

250

Consider a right triangle with a hypotenuse of 4cm. If a height (altitude) is traced from the vertex that has the 90 degrees marked breaking up the opposite side of 4cm into 3cm and 1cm, what is the length of the height of this triangle?

What is 1.7(or square root of 3)?

300

Herminio computed the geometric mean of two numbers. One of the numbers was 7 and the geometric mean turned out to be 7 as well. What was the other number?

What is 7?