Name: _______________________________________________
One special right triangle is an isosceles right triangle, also called a 45° - 45° - 90° triangle. Each isosceles right triangle is half a square, so these triangles show up often in mathematics and engineering.
Step 1: Find the length of the hypotenuse of each isosceles right triangle below. Simplify your square roots!
(NO DECIMALS)

Name: _______________________________________________
Step 2: Use your answers in part 1 to complete the table. Draw additional triangles if needed.
Length of
Each Leg
1 2 3 4 5 6 7
…
10
… x
Length of hypotenuse
Step 3: Discuss the results with your group. Do you see a pattern between the length of the legs and the length of the hypotenuse? State your observations as a conjecture:
Isosceles Right Triangle Conjecture:
In an isosceles right triangle, if the legs each have length s , then the hypotenuse has length a length of _________.
Another special right triangle is a 30° - 60° - 90° triangle. This triangle also shows up often in mathematics and engineering because it is half of an equilateral triangle.
Step 1: Make the following observations of the above diagram:
1.
What is the measure of

C in

ACD ? Why?
2.
How are the lengths of DB and AB related?
3.
How are the lengths of DB and CB related? (Remember:

ABC is an equilateral triangle!)
4.
Use the diagram and your answers for #2 and #3 to make the following observation:
In any 30° - 60° - 90° triangle, how are the length of the hypotenuse and the length of the shorter leg related?

Name: _______________________________________________
Step 2: Use the relationship that you discovered in #4 of step 1 above to a) find the length of the hypotenuse of each 30° - 60° - 90° triangle below. Then, b) calculate the length of the third side (the longer leg) of each triangle. NO DECIMALS!
Step 3: Use your work from step 2 to complete this table. Draw additional triangles if needed.
Length of
Shorter Leg
Length of hypotenuse
1 2 3 4 5 6 7
…
10
Length of
Longer Leg
… x
Step 4: Discuss the results with your group. Do you see a pattern between the length of the longer leg and the length of the shorter leg? State your observations from this investigation as your next conjecture:
30° - 60° - 90° Triangle Conjecture:
In a 30° - 60° - 90° triangle, if the shorter leg has a length s , then the hypotenuse has a length of ________ and the longer leg has a length of _____.
Copy Theorem 8.5 and 8.6 from your book onto your postulates sheets (Pg 425)!