Download 4-4 Proving Triangles Congruent by SSS and SAS 2 THINGS CAN

4-4 Proving Triangles Congruent by SSS and SAS
- ÿ- ÿ ÿ) Co__qEqruence Postulate
If three sides of one triangle are ÿ
to three sides of a second triangle,
then the two triangles are ÿ
.
B
--€
If
then
2 THINGS CAN BE ADDED TO A PICTURE IN A PROOF.
YOUR PROOF MUST CONTAIN STEPS THAT SAY WHAT YOU ARE ADDING.
Triangles that share a ÿ
side. Since the same side is in both
triangles, it can be marked ÿÿ:ÿ> REFLEXIVE PROPERTY
.
angles can be marked ÿ.
Proof Blocks
In Proof Blocks, every theorem, postulate, and definition is represented by a block. These blocks
can either be physical manipulatives, or simply drawn on the page.
'
Here is a link you can check out.
http:llwww.proofblocks.comldetailsldetails/introduction.html
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Example of Proof Blocks: Use SSS Congruence Postulate to Solve:
Given: KL-ÿNL, KMÿMN
N
K
Prove: DKLMÿ A NLM
M
i
-- Picture
Reflexive
Property
--
SSS
ÿ, ÿN
,1ÿ ÿ Postulate
How would this look as a 2-coulmn proof?
i
mÿiÿ: Use SSS Congruence Postulate to solve:
Given: KLÿNL, KM ÿMN,
Prove: A KLM ÿ A NLM
Statements
I, Kt %ÿt
N
K
J
KÿXÿ ÿN
M
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The angle formed by two adjacent sides of a polygon is called the ÿ ÿ1ÿ-ÿ.
Draw an example of included angles:
oÿ - ÿ- ÿ ÿ) Conqruence Postulate
If two sides and the included angle of one triangle are congruent to two sides and the included
angle of a second triangle, then the :two triangles are congruent..
ÿ
s
If
, then
by ÿAÿ
pÿrr.ÿ- _ÿ.[ÿ_ÿÿ) Conqruence Theorem
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a
second triangle, then the two triangles are congruent.
A
D
Reme.mbÿr Rieht ÿldOngleÿ:
E
, then
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Example: Use 5AS Postulate to solve.
B
Given: BC z AD & BC //AD
Prove: zÿABC ÿACDA
Statements
e
ÿ
C
Reasons
A
e
b,
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