Chapter 5 Relationships within Triangles



In class examples:

Day 1: Midsegment Theorem

Midsegment of a Triangle

Practice with midsegment #'s 1-4

Day 2: Coordinate Proof



practice with proofs #'s 5-7

Ch 4 test Review

Ch 4 test review outline


try pg 282 - 285 #'s 1-26 all. Good Luck and Happy studying!!



CPCTC and base angle theorem practice problems

5.7 Quiz

Practice with Proofs

Review homework problems.

Use Congruent Triangles

What you need to know for the quiz tomorrow. How to use and identify the following:

1. SSS
2. SAS
3. AAS
4. ASA
5. HL
6. CPCTC
7. Use Isosceles and Equilateral Triangles

Try the following quizzes for homework tonight.

• 4.3 Prove Triangles Congruent by SSS
• 4.4 Prove Triangles Congruent by SAS and HL
• 4.5 Prove Triangles Congruent by ASA and AAS
• 4.6 Use Congruent Triangles
• 4.7 Use Isosceles and Equilateral Triangles

4.7 Use Isosceles and Equilateral Triangles

Goal • Use theorems about isosceles and equilateral triangles.

Vocabulary

When an isosceles triangle has exactly two congruent sides, these two sides are the legs. The angle formed by the legs is the vertex angle. The third side is the base of the isosceles triangles. The two angles adjacent to the base are called base angles.

Legs
The legs of an isosceles triangle are the two congruent sides.

Vertex angle
The vertex angle of an isosceles triangle is the angle formed by the legs.

Base
The base of an isosceles triangle is the side that is not a leg.

Base angles
The base angles of an isosceles triangle are the two angles adjacent to the base.

In class examples (click for link)


Lesson 7 Examples 1-4

4.6 Use Congruent Triangles

Key Concept

Once you have proved that two triangles are congruent, you know that their corresponding parts must be congruent as well. This will allow you to find the unknown measures of angles , objects and distances, as well as prove that constructions of copying angles are valid.

Goal: Use congruent triangles to prove corresponding parts congruent.

4.5 using congruent triangles

View more presentations from Jessica Garcia.

Working with Congruent Triangles in Proofs

Remember when working with congruent triangles...

1. Mark any given information on your diagram.
2. Look to see if the pieces you need are "parts" of the triangles that can be proven congruent.
3. If not given all needed pieces to prove the triangles congruent, look to see what else you might know about the diagram.
4. Know your definitions! If the given information contains definitions, consider these as "hints" to the solution and be sure to use them.
5. Stay open-minded. There may be more than one way to solve a problem.
6. Look to see if your triangles "share" parts. These common parts are automatically one set of congruent parts.

Example 1: How do we decide which method we should be using?

Example 2: Numerical Practice with Congruence


Quiz Monday

Practice with Congruent Triangle Proofs

Practice with Beginning Congruent Triangle Proofs

Directions: When attempting to prove triangles congruent, it is important to satisfy all of the conditions of the congruent triangle method you are using. This activity is designed to help you organize your thinking about how the parts of a congruent triangle proof will come together. In each problem below, examine the diagram and the GIVEN information. You may wish to draw the diagrams on paper so that you can mark off the information.

• Determine the method needed to prove the triangles congruent.
  (ASA, SAS, AAS, SSS, or HL for right triangles only)

• Check to see if you have the correct method by looking at the Method for Congruent Triangles box at the bottom of the chart.

• Each of the three components needed to support the chosen method appear to the left of their corresponding Statement.

• Decide what Reasons can be used to support your decisions.

Recognizing Congruent Triangles (click to see in class examples)

Example 1: Prove Triangles are Congruent

Homework:
Do the following problems below. I will collect this assignment Monday.

Directions:

1. Copy down each diagram or print the sheet.
2. Mark up the diagram.
3. Fill in all the blanks.
4. 
   

4.1 and 4.2 Quiz

Triangles Congruence Theorems (SSS, SAS, ASA, HL)

Methods for Proving Triangles Congruent

Goal:

Learn Different methods to prove triangles are congruent using:

1. Side Lengths
   
2. Side Lengths and Angles
   

Provingtrianglescongruentssssasasa

View more presentations from Jessica Garcia.

In summary, when working with congruent triangles, remember to:

1. Mark any given information on your diagram.
2. Look to see if the pieces you need are "parts" of the triangles that can be proven congruent.
3. If not given all needed pieces to prove the triangles congruent, look to see what else you might know about the diagram.
4. Know your definitions! If the given information contains definitions, consider these as "hints" to the solution and be sure to use them.
5. Stay open-minded. There may be more than one way to solve a problem.
6. Look to see if your triangles "share" parts. These common parts are automatically one set of congruent parts.
   

Remember that proving triangles congruent is like solving a puzzle. Look carefully at the "puzzle" and use all of your geometrical strategies to arrive at an answer.

4.2 Apply Congruence and Triangles

In class examples: lesson 2 examples 1-5

4.1 practice Quiz

4.2 practice Quiz

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TRIANGLES

Triangles Representation



Triangle Song


4.1 Apply Triangle Sum Properties

Chapter 4 Congruent Triangles

Big Ideas

1. Classifying triangles by sides and angles
2. Proving that triangles are congruent
3. Using coordinate geometry to investigate triangle relationships
   

In class problems: Do workbook pg 61-63 #'s 5-8, 11-15 odd 21 -26 all.

Finish workbook problems for homework.