section 4 4 proving congruence sss, sas€¦ · · 2015-01-30section 4 4 proving congruence ...
Post on 14-May-2018
228 Views
Preview:
TRANSCRIPT
1
2
Section 4 4 Proving Congruence SSS, SAS
Today we will learn 2 shortcut ways to show that 2 triangles are congruent.
It is not always necessary to show that all of the corresponding parts of two triangles are congruent to prove that the triangles are congruent.
Instead of showing 6 pairs of congruent parts, we only have to show 3 pairs of congruent parts.
In this lesson, we will explore two other methods to prove that triangles are congruent.
If the corresponding sides of two triangles are congruent, then the triangles are congruent.
This is the Side Side Side Postulate, and is written as SSS.
3
Ex 1 Determine whether for R (2 , 5),Z (1 , 1) , T(5 , 2) , L ( 3, 0) , K (7 , 1) , and J(4 , 4). Explain.
Hint: Use the distance formula to show that the corresponding sides are congruent.
4
You will be asked to some proofs in your homework for the rest of this chapter.
Anytime that you are asked to do a flow proof or a paragraph proof you are going to do a twocolumn proof.
Make sure that you get in the habit of using the diagrams on these proofs.
Ex 2 Given:
Prove:
Statements Reasons
5
Ex 3 Given: V is the midpt of RT
Prove:
Statements Reasons
6
Suppose you are given the measures of two sides and the angle they form, called the included angle.
These conditions describe a unique triangle.
Two triangles in which corresponding sides and the included pairs of angles are congruent provide another way to show that triangles are congruent.
This is known as the SAS Postulate.
7
Ex 4 Given:
Prove:
Statements Reasons
8
Ex 5 Given: X is the midpoint of BD. X is the midpoint of AC.
Prove:
Statements Reasons
9
Remember that CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent".
Today we are going to be using CPCTC in our proofs.
First of all, you will have to prove that 2 triangles are congruent by either SSS, SAS, AAS, or ASA.
Then you can use CPCTC in the step after proving that the two triangles are congruent.
Once you know that 2 triangles are congruent, you can then use CPCTC to say that corresponding parts of the two triangles are also congruent.
10
Ex 6 Write a twocolumn proof.Take the 2 triangles apart!!!
Given:
Prove:
Statements Reasons
11
Ex 7 Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible.a.
b.
c.
d.
12
Ex 7 (continued)e.
f.
g.
h. Sometimes it is necessary to take 2 triangles apart to see if they are congruent.
Assign Pgs. 203 206 # 2, 5 12, 14 16, 18, 21 25, 31 40 44 47
IMPORTANT NOTE: Anywhere they ask you to do a paragraph proof or a flow proof, I want you to do a twocolumn proof instead.
top related