# Geometry 4-5 More Congruent Triangles by cometjunkie43

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```									Geometry 4-5 More Congruent Triangles

A. Current Congruences
1. We know three ways to prove triangles congruent so far. They are ________________,
______________, and _______________.

B. Postulate 4-3 ASA Postulate ( _________-_________-__________ Postulate)
-If two angles and the __________ side of one triangle are congruent to two angles and the
___________ side of another triangle, then the triangles are _____________.
C
Ex. 1:                                        A
1
<A≅<D                                                  E
Prove:     AB ≅ DC                                                             D
B

Statements                                            Reasons
<A≅<D
2.)                                                   2.) Vertical <’s are ≅
3.) AE ≅ ED                                           3.)
4.) ∆ AEB ≅ ∆DEC                                      4.)
5.) AB ≅ DC                                           5.)

C. Theorem 4-5 AAS Postulate ( _________-__________-________ Postulate)
-If two angles and a_____________ side of one triangle are congruent to the corresponding
two angles and a_____________ side of a second triangle, then the two triangles are
___________.
S                         T                                    T
S
Ex. 2: Write a proof

Given:     < PSU ≅ < PTR            R                 U                            U   R
SU ≅ TR
Prove:     SP ≅ TP
P                               P                P

Statements                                            Reasons
1.) < PSU ≅ < PTR                                     1.)
SU ≅ TR
2.)                                                   2.) Reflexive
3.)                                                   3.)
4.) SP ≅ TP                                           4.)
Ex. 3: Some of the measurements of ∆ ABC and ∆ DEF are given. Can you determine if the
two triangles are congruent?
C                                F

2.5                              2.5

40°                              40°
A                         B      D                               E
4.0                              4.0

Explore: Since we know < A ≅ < D, and we know AB ≅ DE, and CB ≅ FE ; we know that
there are two congruent sides and one non-included angle that are congruent. Our five
methods of proving triangles are:

1.)   definition of congruent ∆’s (all 3 sides and all 3 angles)
2.)   SSS congruence
3.)   SAS congruence
4.)   ASA congruence
5.)   AAS congruence

-     since none of these work, the triangles must not be congruent.

Counter Example: here is a case where the triangles are obviously not congruent, but the
same conditions hold true.

Y

C                                          W               2.5
2.5

40°                                        40°
A                         B                X                               Z
4.0                                          4.0

HW: Geometry 4-5 p. 211-213
9-11 all, 15-16 (two column), 23-28 all, 31-33 all, 35-41 all

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