Special Right Triangles Flashcards
Isosceles Right Triangle
Both angles are 45
Two sides are equal
45 45 90 Triangle
They hypotenuse is what one of the legs is * sqrt of 2
So leg = a , other leg = a and hypotenuse = a sqrt 2
If the hypotenuse of an Isosceles Right Triangle is 12, what are the two legs?
leg each equal 6 sqrt 2
basically you divide 12 by sqrt of 2 and simplify to find the legs
Anytime you put a diagonal through a square, what are you creating?
A pair of 45 45 90 triangles
30 60 90 Right Triangle
30 60 90 Right Triangle
Everything in this triangle is based off the smallest side = a
Hypotenuse = 2a
The other one is a * sqrt 3
In a 30 60 90 Triangle if the smallest side is 4 what are the other two sides?
Hypotenuse = 8
Other side = 4 sqrt 3
What are the angles equal to in a equilateral triangle?
60 degrees
Where is the most common place to see a 30 60 90 Triangle?
In a parts of a equilateral triangle
and figuring out the area of a equilateral triangle
If the height of a triangle is 6 and the base of the triangle is 6 + 6 sqrt 3 then what is the area of the triangle?
Area = 18 + 18 sqrt 3
Third side rule (applies to any triangle)
The third side of any triangle is bigger than the difference of the other two sides and smaller than the sum of the other two sides
So if you had one side = 5 and the other = 8 and the last side = x then x must be > 3 and x is < 5 + 8
Perimeter = ?
Sum of all the sides
How is the Third Side Rule related to finding the perimeter?
If you have a triangle with one unknown side, x and the other side 5 and the other side 8, you might not know what x is but you know the range that x has to be so x > 3 and x < 5 + 8
If the two sides of a right triangle measure 3 inches and 4 inches, respectively, then which of the following statements must be true?
A. The third side measures 5 inches
B. The length of the third side is less than 7 inches long
C. The length of the third side is greater than 1 inch thick
Answers = B and C
Use the third side rule 3+4 = 7 and 4-3 = 1 so the third side has to less than 7 and greater than 1
In a triangle (with no additional information about angles) there are three angles, a, b and c. Angle b = 35 degrees. In terms of c, which of the following expressions are possible values for a?
A. c - 90
B. c + 90
C. c - 150
D. 3c
indicate all
Answers = A, B, and D
Since it does not say that the sides have to be integers, use FROZEN values such as c = 117.5 and a = 27.5 knowing that the sum has to equal 145 (since 180 - 35 = 145)
for B try c = 27.5 and then c = 117.5
For D try c = 36.21 and a = 108.75
square WXYZ is inscribed in equilateral triangle ABC
QA: 150
QB: The sum of the degree of measurements of angle WXY and angle ABC
Answer = the two quantities are equal!
Not even necessary to draw a picture as a square always has 4 equal angles of 90 degrees and an equilateral triangle has 3 equal angles of 60 degrees each. SO 90 + 60 = 150 and they are equal
