Transcript 3.5 Overlapping Triangles

3.5
Overlapping
Triangles
Steps:
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1.
Mark the given information on your
diagram and write the givens in your proof.
2. Do anything the givens tell you to do (aka if
given bisection, state the now congruent segments or angles).
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3. Decide which triangles you will be able to
prove congruent.
4. Re-Draw the triangles our corresponding and
hopefully use CPCTC to finish the proof.
P
Given : PW TM
PM TW
Prove : P  T
S
T
M
W
1. Mark the given information.
2. Decide which triangles we can prove congruent.
PWM and TMW
3. Re-Draw the triangles so they are corresponding
T
M
W
P
Given : PW TM
PM TW
Prove : P  T
M
W
M
Reasons
Statements
1.
PW TM S1 
PM TW
1.
Given
2.
Reflexive Prop.
S 
2. WM  MW
2
S 
3
3.
PWM  TMW
3.
SSS
4.
P  T
4.
CPCTC
T
W
F
Given : FGH is a rt . angle
JHG is a rt . angle
J
K
FG  JH
Prove : FGH  JHG
H
G
1. Mark the given information.
2. Decide which triangles we can prove congruent.
FGH and JHG
3. Re-Draw the triangles so they are corresponding
J
H
G
Given : FGH is a rt . angle
JHG is a rt . angle
FG  JH
Prove : FGH  JHG
F
J
Reasons
Statements
1. FGH is a rt . angle
JHG is a rt . angle
FG  JH
H
1. Given
S 
1
2. FGH  JHG
3. GH  HG
H
G
S 
2
4. FGH  JHG
A 
1
2. If 2 angles are rt. angles, then
they are congruent.
3. Reflexive Prop.
4. SAS
G
Given : NOPRS is equilateral
N
OPR  PRS
PT TR
S
O
Prove : OT TS
T
P
1. Mark the given information.
R
2. Decide which triangles we can prove congruent.
OPR and SRP
3. Re-Draw the triangles so they are corresponding
S
T
R
P
N
Given : NOPRS is equilateral
OPR  PRS
PT TR
O
T
Prove : OT TS
P
1. NOPRS is equilateral
OPR  PRS A1 
T
R
Statements
S
O
S
R
T
P
Reasons
P
1. Given
R
PT TR
2. OP  SR
S 
3. PR  RP
S 
1
2
2. If a figure is =lateral, then all sides are
congruent.
3. Reflexive Prop.
4. OPR  SRP
4. SAS
5. OR  SP
5. CPCTC
6. OT TS
6. Subtraction Property
OR TR  OT 


 SP  PT TS 


If congruent segments are subtracted from
congruent segments, then their differences
are congruent.
Homework
p. 135 # 5 – 11 odd
 p. 140 # 5, 9 – 12
 Study for QUIZ!!!!!
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