4.4 and 4.5 triangle congruence conjectures.web.cerritos.edu/dford/sitepages/fall2011/math70lecture...
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4.4 and 4.5 TRIANGLE CONGRUENCE CONJECTURES.
Ways to show two Triangles are Congruent:
Side-Side-Side Side-Side-Angle Side-Angle-Angle
Angle-Angle-Angle Angle-Side-Angle Side-Angle-Side
A C
C
A C
C
A
Construct a triangle, more than one if possible, using the following:
a) b) c)
Draw a triangle with the following interior angles 45, 45, 90.
Why did SSA not work?
Why did AAA not work?
A B
A C
B C
A B
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Mark the following triangles given the stated congruent triangle conjecture.
DEF
SSS SAA
ASA SAS
Determine which triangles are congruent and why?
Using your previous conjectures mark congruent angles and sides if they exist and then find the corresponding congruent triangle. State the reason the two triangles are congruent.
A
B C
E
D F
A
B C
E
D F
A
B C
E
D F
A
B C
E
D F
1 OHW ___________
Which conjecture supports the congruence statement?(if not enough info, write not enough info) _________
2. sAB // sCD ( hint: transversal?), sAD sBC , ABC ___________
Which conjecture supports the congruence statement?(if not enough info, write not enough
info) _________
3. sAC sBD, sAD sBC, ADB ___________
Which conjecture supports the congruence statement? _________
a a
A B
C D
a a
A
C
E
D
B
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5. sQD sAD, sQU sAU If you construct segment DU, you can show QDU ADU.
Which conjecture tells you they are congruent? ______
6. sAB sCD, CDB ABD
Which conjecture tells you that ABD CDB? _________
a a
Q
A
D
U
a a
A C
E
D B
10. which conjecture supports each congruence statement?
ABH CBD _________
HGF DEF _________
HFB DFB _________
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a a
P R
S
Review:
Construct the ABC so that it is congruent to PSR using ASA
Construct the ABC so that it is congruent to PSR using SSS
Construct the ABC so that it is congruent to PSR using SAS
4.6 CPCTC 1. ABC _______. Which conjecture supports the congruence statement? _________
A B
D
C
Because of ___________ both triangles are congruent. Which means
BDCCABandBCACBDsDBsAC ,,
CPCTC ----- Corresponding Parts of Congruent Triangles are Congruent
2. ABC _______
Which conjecture supports the congruence statement? __________
A
B
C E
D
Because of ___________ both triangles are congruent. Which means
BCADCEandDBsDCsBCsEDsAB ,,,
3. sAB sCD, sAB sCD, EC sCD, A D, ABC _______
Which conjecture supports the congruence statement? _________
Because of ___________ both triangles are congruent. Which sides and angles are congruent?
a a
A B
C
D
E
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H
R
GIVEN
GIVEN
KO
4.7 FLOWCHART THINKING
1. Provide each missing reason or statement in the flow-chart proof.
Given: sHR sSE
R S
Show: sHU sEU
S
Flow-chart Proof: E U
5. From the picture fill in the given and
Prove: KO
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GIVEN
GIVEN
GIVEN
GIVEN
GIVEN
GIVEN
6. Find the two congruent triangles and draw them next to each other, then write a proof.
Given: sPR sPQ
sPT sPS
Prove: PRT PQS
7. From the picture fill in the given and
Prove: sYWsOW
8. Given: D C
sDE sEC
Prove: sAE sBE