Download Congruence Criteria for Triangles – AAS

Name: ______________________________________________________________________
Date: _____________
Congruence Criteria for Triangles-AAS
Geometry CC (M1-L25)
Congruence Criteria for Triangles – AAS
Opening Exercise
Example #1: Write a proof for the following question. When finished, compare
your proof with your partner’s.
Given: DE
Prove:
DG , EF
GF
DF is the angle bisector of EDG
a. Using these triangles, we can see there is a rigid motion that will map DEF to DGF . Name that rigid motion and
also show using function notation.
b. We have identified 3 different ways of proving triangles congruent. What are they?
c. Does this mean any combination of 3 pairs of congruent sides and/or angles will guarantee congruence?
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Let’s try another combination:
Angle-Angle-Angle (AAA)

All three pairs of angles are congruent http://www.mathopenref.com/congruentaaa.html
Does AAA guarantee triangle congruence? Draw a sketch demonstrating your answer.
---------------------------------------------------------------------------------------------------------------------------------------------------------------Let’s take a look at one more combination of sides and angles criteria:
Angle-Angle-Side Triangle Congruence Criteria (AAS)

Two pairs of angles and a side that is not included are congruent
To show this criteria is a valid method for proof we could start with two distinct triangles.
a. If
B
E and
C
F , what must be true about
A and
D ? Why?
b. Therefore, AAS is actually an extension of which triangle congruence criterion that we have already
mentioned?
---------------------------------------------------------------------------------------------------------------------------------------------------------------Angle-Angle-Side Triangle Congruence Criteria (AAS):
Given two triangles 𝐴𝐵𝐶 and 𝐴′𝐵′𝐶′.
If
B
C
and AB
B ' (______),
C ' (______),
A ' B ' (_______)
then the triangles are ______.
2
Use your knowledge of triangle congruence criteria to write proofs for each of the following problems.
Example #2:
Given: BC
Prove:
CD, AB
BCD
AD, 1
2
BAD
Describe the rigid motion(s) that would map BCD onto BAD .
---------------------------------------------------------------------------------------------------------------------------------------------------------------Example #3:
Given: ∠𝐴 ≅ ∠𝑃, ∠𝐵 ≅ ∠𝑅, 𝑊 is the midpoint of ̅̅̅̅
𝐴𝑃
̅̅̅̅̅
̅̅̅̅̅
Prove: 𝑅𝑊 ≅ 𝐵𝑊
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Name: ______________________________________________________________________
Day 35: HOMEWORK
Date: _____________
Triangle proofs summary THUS FAR. Let’s see what you know!
1. List the 4 ways of proving triangles congruent we have thus far:
1.
2.
3.
4.
2.What set of criteria, that we discussed in class today, CANNOT be used to prove triangles congruent:
1.
3.. In order to prove a pair of corresponding sides or angles are congruent, what must you do first?
Use your knowledge of triangle congruence criteria to write a proof for the following problem.
4.
Given: AD
1
Prove: AE
BC
2
BE
Describe the rigid motion(s) that would map ADE onto BCE .
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Name: ______________________________________________________________________
Day 35: EXIT TICKET
Given: AB BC, DE
Prove: ABC
DEF
EF , BC EF , AF
DC
Name: ______________________________________________________________________
Day 35: EXIT TICKET
Given: AB BC, DE
Prove: ABC
DEF
EF , BC EF , AF
Date: _____________
Date: _____________
DC
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