Download 4.2 Some Ways to Prove Triangles Congruent

1. If two triangles are congruent, then they
have matching________ and ________.
2. Complete the congruence statement.

1. T
2. m I
3. CA
4. IG
5. ΔATC
6. ΔBGI
7. E, F, S, T
8. Definition of  Δs
9. L F,  X  N, R  E,
LX  FN, XR  NE, LR  FE
10.a. ΔKRO
b. K, CPCT
c. KO, CPCT
d. R, CPCT Alt Int s are 
11.a. ΔRLA
b. RL
c. 3, CPCT
LR, Alt Int s are 
d. 4, CPCT
PL, AR, Alt Int s are 
Section 4-2 Some Ways
to Prove Triangles
Congruent
When we talk about congruent triangles,
we mean everything about them is congruent.
All 3 pairs of corresponding angles are equal….
And all 3 pairs of corresponding sides are equal
For us to prove that 2 people are identical
twins, we don’t need to show that all “2000”
body parts are equal. We can take a short
cut and show 3 or 4 things are equal such
as their face, age and height. If these are
the same I think we can agree they are
twins. The same
is true for triangles. We don’t need to prove
all 6 corresponding parts are
congruent. We have 5 short cuts or
methods.
Today we will look at 3 methods.
SSS
If we can show all 3 pairs of
corresponding sides
are congruent, then
the triangles are congruent.
SAS
If we can show 2 pairs of sides and the
included angles are congruent, then
the triangles are congruent.
Included
angle
Non-included
angles
This is called a common side.
It is a side for both triangles.
We will be using the reflexive property
to state the common side.
If two angles and the included side of one triangle are congruent
to two angles and the included side of another triangle, then the
triangles are congruent.
M
Y
N
Z
L
X
XYZ ~=
LMN by ASA Post.


Vertical Angles are ≅
Angles pairs formed when two lines are
parallel.
◦ Alternate Interior Angles
Which method can be used to
prove the triangles are congruent?
Common side
SSS
Vertical angles
Parallel lines
alt int angles
Common side
SAS
SAS
Tick Mark Common Side
Yes ≅
by SAS
Tick Mark
Common
Side
NOT ≅
Tick Mark
Common
Side
Yes ≅
by SSS
|| Lines-Alt Int.
∠𝑠 ≅
Common Side
Yes ≅
by SAS
Common Side
Yes ≅
by ASA
 You
must use theorems,
postulates, and definitions to
deduce sides/angles are
congruent.
 “It looks the same” will not
suffice.
T
Given: E is the midpoint of MJ;
TE ⊥ MJ
M
Prove: ∆𝑀𝐸𝑇 ≅ ∆𝐽𝐸𝑇

E
Statements
Reasons
1. E is the midpt. of MJ.
1. Given.
2. 𝑀𝐸 ≅ 𝐸𝐽
2. Def. of midpt.
3. TE ⊥ MJ
3. Given
4. ∠𝑀𝐸𝑇 ≅ ∠𝐽𝐸𝑇
5. TE=TE
4. If two lines are ⊥, then
they form ≅ adj. ∠s
5. Reflexive Prop.
6. ∆𝑀𝐸𝑇 ≅ ∆𝐽𝐸𝑇
6. SAS Postulate
J


Pg 124-126 Written Exercises
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