Converse of the Pythagorean Theorem
Pacing:This lesson should take one class period
Goal:This lesson applies the converse of Pythagorean’s Theorem to determine whether triangles are right, acute, or
obtuse.
Additional Examples:
a. Can the following lengths form a right triangle? Explain your answer. 10, 15 , 225 .No, 102 + 152 = 325 .However,
this will be much less than 2252.
b. Find an integer such that the three lengths represent an acute triangle: 9, 12 ,____.Sample: 16 , 17 , 18 , 22 ...
c. Find an integer such that the three lengths represent an obtuse triangle: 8, 19 ,____.Sample: 20 , 10 , 14 ,...Using Similar Right Triangles
Pacing:This lesson may take two class periods, due to the difficulty of the material
Goal:The concept of geometric mean is used in Advanced Algebra to determine the mean of a widespread data set.
In geometry, the geometric mean is illustrated using a right triangle and its altitude.
Look Out!The concept of geometric mean is easy to comprehend, but difficult for student to apply. Spend time in
class reviewing this lesson and using additional examples.
An alternative to the abstract formula for geometric mean is, “The altitude of the hypotenuse equals the geometric
mean between the segments of the hypotenuse.”
Additional Examples:
a. Consider the diagram below. Supposeh=12 andx=8. Findy.y= 18
b. Consider the diagram below. Supposea=?,x=9 andy=11. Find the value ofa.a= 6√
5
c. Consider the diagram below. Supposex=5 andy= 15 .Find the value of the altitude,h.h= 5√
3
Special Right Triangles
Pacing:This lesson should take one class period
Goal:The purpose of this lesson is to encourage the use of shortcuts to find values of special right triangles. These
triangles are extremely useful when relating the trigonometric functions to the exact values found within the unit
Chapter 1. Geometry TE - Teaching Tips