Name: Date: Day 6: Triangle Congruence, Correspondence and ...
Name: ____________________________________________ Day 6: Triangle Congruence, Correspondence and Styles of Proof
Opening Exercise
Given: CE bisects BD
Statements
1. CE bisects BD
2.
1.Given 2.
Reasons
Date:______________ Geometry CC (M1D)
Define congruence in your own words:
Define congruence using your knowledge of basic rigid motions:
--------------------------------------------------------------------------------------------------------------------------------------------------In order to prove triangles are congruent, we do not need to prove all of their corresponding parts are congruent. Instead we will look at criteria that refer to fewer parts that will guarantee congruence. There are 5 ways to prove triangle congruence.
1. SAS SAS _____________________________________________
2. SSS SSS _____________________________________________
3. ASA ASA ____________________________________________ 4. AAS AAS ____________________________________________
5. HL HL _____________________________________________
Two sets of criteria that are NOT SUFFICIENT in proving triangles congruent are 1. AAA AAA_____________________________________________
2. SSA SSA _____________________________________________
1
Three things to look for when proving triangles congruent:
Vertical Angles
Reflexive Property (Shared Side)
Reflexive Property (Shared angle)
---------------------------------------------------------------------------------------------------------------------------------------------------------------Example 1: If they pairs of triangles below are congruent, then name their congruence criteria. (SSS, SAS, ASA, AAS, HL) If not, state that it is not sufficient to prove that the triangles are congruent.
Example 2: In the diagram of ABC and DEF below a sequence of rigid motions maps , AB onto DE , A D, and B E. Which method can be use to prove ABC DEF ?
1) AAS AAS 2) SAS SAS
3) SSS SSS 4) ASA ASA
b) Determine and state whether AC DF . Explain why. 2
Practice NYTS (Now you try some!)
1. Are the following pairs of triangles congruent? If they are, then name their congruence criteria.
(SSS, SAS, ASA, AAS, HL)
a) Yes / No __________
b) Yes / No __________
c) Yes / No __________
d) Yes / No __________
e) Yes / No __________
f) Yes / No __________
g) Yes / No __________
h) Yes / No __________
2. If you are given that
and
which additional statement is sufficient evidence that
to
by only the SAS SAS criteria?
is congruent
1) AC DF
2) 3) 4)
3. If you are given that
, and
which additional statement is sufficient evidence that
is
congruent to
by only the AAS AAS criteria?
1) AC DF
2)
3) AB DE 4) BC EF
4. In the diagram below of
and
, a sequence of rigid motions maps onto , onto , and
onto .
Are
and
congruent? If so, name the method.
Determine and state whether
. Explain why
3
STYLE 1:_________________________
STYLES OF PROOFS
STYLE 2:_________________________
STYLE 3:_________________________
STYLE 4:________________________
4
Name: ____________________________________________________ Day 7: Congruence Criteria for Triangles- SSS Opening Exercise
1. What are the 5 ways to prove triangles are congruent?
2. What do we use instead of SSA? When do we use it?
3. What 3 things do we check for when we are out of givens?
Date:______________ Geometry CC (M1D)
4. In the diagram below of and onto .
and
, a sequence of rigid motions maps AB onto XY , BC onto YZ ,
Determine and state whether C Z . Explain why.
---------------------------------------------------------------------------------------------------------------------------------------------------------------Side-Side-Side triangle congruence criteria (SSS): (All three sides are )
-------------------------------------------------------------------------------------------------------------------------B--------------------------------------
Example 1: In the diagram below AB BC , D is the midpoint of AC Prove that ABD CBD
1. AB BC
Statements
2. D is the midpoint of AC
3. AD DC
4. BD BD 5. ABD CBD
A
D
C
Reasons
1.
2.
3.
4.
5.
b) Precisely describe the rigid motion(s) that would map ABD onto CBD . 5
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