Name _____________________________ Period
Geometry
Date ___________________________Mrs. Schuler
TriangleTest 3 Review Sheet
1. Special Right Triangles
45/45/90
a. Know the principle: In a 45/45 90 triangle the legs are congruent and the hypotenuse is
equal to leg√2
b. Find the perimeter of a square give the diagonal.
c. Know the ratio table and how to apply it
45
45
90
X
x
x√2
d. Solve for the length of a side given one side – use ratio table to set up
2. Special Right Triangles
30/60/90
a. Know the Principle: In a 30/60/90 triangle the hypotenuse is twice the smaller leg and the
smaller leg is half the hypotenuse. The larger leg is equal to the smaller leg√3.
b. Know ratio table and use it to find the length of missing side
30
60
90
X
x√3
2x
3. Mean Proportional (Geometric Mean)
Know how to set up proportion and solve.
4. Right Triangle with Altitude and Segments
a. Know Principle: In a right triangle with an altitude drawn from the right angle to the
hypotenuse, the altitude is geometric mean (aka mean proportional) of the hypotenuse
segments.
ℎ𝑦𝑝 𝑠𝑒𝑔
𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒
b. Know Principle Formula and apply it (including a quadratic): 𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒1 =ℎ𝑦𝑝 𝑠𝑒𝑔
2
5. Right Triangle with Leg and Projection
a. Know Principle
b. In a right triangle with an altitude drawn from the right angle to the hypotenuse each leg is
the geometric mean (aka mean proportional) between the hypotenuse and the projection
of the leg.
c. Know Principle Formula and apply it:
6. Similarity in triangles.
𝑝𝑟𝑜𝑗𝑒𝑐𝑡𝑖𝑜𝑛
𝑙𝑒𝑔
𝑙𝑒𝑔
=ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒