Inequalities in Two Triangles
Pacing:This lesson should take one class period
Goal:The purpose of this lesson is to utilize the concept of inequality to determine corresponding angle measures
and side lengths of a triangle.
Review!Be sure your students can solve inequalities. Try these as a warm-up or brief review.
a. 8x− 4 +x>− 76 x>− 8
b.− 3 ( 4 x− 1 )≥ 15 x≤− 1
c. 8y− 33 >− 1 y> 4Additional Examples:
List the sides of each triangle in order from shortest to longest.
- 4 ABCwithm^6 A= 90 ,m^6 B= 40 ,m^6 C= 50. AC,AB,BC
- 4 XY Zwithm^6 X= 51 ,m^6 Y= 59 ,m^6 Z= 70 .Y Z,X Z,XY
List the angles of the triangle in order from largest to smallest.
- 4 ABCwhereAB= 10 ,BC= 3 ,andCA= 9.^6 C,^6 B,^6 A,
Indirect Proof
Pacing:This lesson should take one class period
Goal:Students have seen several theorems proven using the indirect proof. Indirect proof is an invaluable resource
to students attempting to prove theorems or postulates.
Indirect proofs typically have four sentences that can be summarized by the following acronym: ATBT.
A – Assume (the opposite of what you’re trying to prove. Essentially, this is the negation of the conclusion of the
conditional)
T – Then (by doing some mathematics or using reasoning, a conclusion can be made)
B – But (here lies the contradiction. The conclusion you made in the previous sentences defies a definition or
previously proved theorem)
T – Therefore (your original conditional must be true)
Chapter 1. Geometry TE - Teaching Tips