Lesson Plan
Lesson: Inequalities and Triangles
Length: 45 minutes
Age or Grade Level Intended: High school Geometry
Academic Standard(s):
G.4.8 Prove, understand, and apply the inequality theorems: triangle inequality, inequality in one triangle, and hinge theorem.
G.8.7 Construct logical arguments, judge validity, and give counterexamples to disprove statements.
Performance Objective(s):
The class will be able to orally answer questions that involve finding an angle and side of a triangle with 80% accuracy when given the definition of inequalities and Inequality Theorems.
The class will be able to provide logical arguments that explain why certain angles and sides are bigger or smaller than each other two out of three times.
Assessment:
Orally ask random students to find an angle or side of a triangle and make sure 12 out of the 15 students get the side or angle correct.
Orally ask for logical arguments to support why certain angles and sides are bigger and smaller than others two out of three times.
Advance Preparation by Teacher:
Prepare examples to write on the board.
Attached on note cards
Procedure:
Introduction/Motivation:
We are going to explore Inequalities and Triangles. This lesson will lead up being able to solve problems that involve triangles that can come from real life situations such as architecture and geography.
Step-by-Step Plan:

1.
Present the Definition of Inequalities: for any real numbers a and b, a
> b if and only if there is a positive number c such that a = b + c.
2.
Explain with numbers because with letters some students can get confused .
Example: 6 > 4 because 6 = 4+2
3.
Have students turn to the properties of inequalities on page 247 of text book.
4.
These inequality properties are ones they have seen in previous algebra classes.
5.
Stress the transitive property because that is probably the one they will use when giving reasoning for the inequality between angles and side.
6.
Question: Can someone choose three numbers that would exemplify
the transitive property of inequalities? (Bloom: Application)
Example 6 > 4 4 > 2 therefore 6 > 2
7.
Question: Are there any questions about these properties or the
definition of an inequality?
8.
Present the Exterior Angle Inequality Theorem: if a triangle has an exterior angle, then it is always greater than either of its corresponding remote interior angles.
9.
Question: Is there anyone can remember back in Chapter 4 another
theorem that dealt with exterior angles?(Bloom: Knowledge)
10.
Answer is the Exterior Angle Theorem on page 186 that states the exterior angle is equal to the sum of the two remote interior angles.
11.
So if an exterior angle is the sum of two other angles the exterior angle is bound to be larger than one of the angles on its own.
12.
Example using attached note card labeled #1.
13.
Have students turn to a neighbor and come up with as many inequality statements about the triangles angles. Have a group share a few statements. (Gardner: Interpersonal)
Some answers are provided and they could use the transitive property to give more. Just get maybe two or three statements and make sure they can provide reason using the Exterior Angle
Inequality Theorem.
14.
Introduce new theorem Thm: The angle opposite the largest side will be the largest angle. The word largest can be replaced by medium and smallest.
15.
Draw a triangle with sides and angles that is difficult to tell which side and angle is the longest. (this triangle can be seen on note card #3) If we look at this triangle with no numbers it is going to be hard to tell

what angle is the biggest or which side is the longest. However, knowing this theorem and given the lengths of this triangle we can compare each side and angle.
16.
Question: What side is the largest, middle, and smallest? (Bloom:
Knowledge) label each side L,M,S (largest, middle, smallest).
17.
Question: Now using this new theorem who can tell me the largest,
middle, and smallest angle and explain why? (Bloom: Application)
Answers on card #4.
18.
We can also use this same theorem backwards and states Thm: The side opposite the largest angle will be the largest side.” Again we can say this theorem by replacing largest by middle and smallest.
19.
If we look at a triangle without sides but with angles (Seen on card
#5).
20.
Question: Now using this new theorem who can tell me the largest,
middle, and smallest side and explain why? (Bloom: Application)
21.
Another example: Applying the last theorem explained. (Found on card #6)
Question:
( Bloom: Application)
Determine the inequality relationship between :
DH and GH, DE and DG, EG and FG, DE and EG
Answers with explanation on card.
22.
Another example: Applying Exterior Angle Inequality Theorem.
Question: What angles are less than angle 1? (Bloom:
Application)
Answer is on card. (card #7)
23.
Assign homework assignment located on card #8.
Closure:
Tomorrow we will go over your homework and move into section 5.3. You will need to master applying these theorems in order to understand the next section so make sure if you have any questions while working on your homework you ask me.
Adaptations/Enrichment:
Girl with ADHD-Hyperactive: Make sure she does not sit by other students that could be distracting and encourage her to not pay attention. Be sure to continuously ask her questions to keep her attention.
Boy with Autism: Prepare him with typed notes so that he knows the routine that is going to take place. Also when given homework to work on

at the end of class allow him to go with his aide to have one-on-one assistance.
Boy with High Ability: Keep him involved in the examples so he doesn’t start to day dream. Give him challenge problems as an extension to the homework assignment.
Self-Reflection:
I will be able to evaluate the lesson and my teaching by:
1.
How well the students respond to the examples and questions
2.
How well students do on the homework assignment
3.
How many questions were asked during the lesson
4.
How smooth the presentation went
Self-Reflection: