pg 245 - San Juan

PROBLEM SOLVING
CONGRUENT TRIANGLES In Exercises 31 and 32, identify the theorem or
postulate you would use to prove the triangles congruent.
31.
32.
B
E
B
A
C
A
E
D
C D
F
F
B
D
C
F
B
E
E
A
A
D
C
F
33. SAILBOATS Suppose you have two sailboats. What information do
you need to know to prove that the triangular sails are congruent
using SAS? using HL?
GPSQSPCMFNTPMWJOHIFMQBUDMBTT[POFDPN
EXAMPLE 3
on p. 242
for Ex. 34
34. DEVELOPING PROOF Copy and complete the proof.
GIVEN
L
LN.
c Point M is the midpoint of }
nPMQ is an isosceles triangle with base }
PQ.
∠ L and ∠ N are right angles.
PROVE c n LMP > n NMQ
STATEMENTS
REASONS
1. ∠ L and ∠ N are right angles.
2. nLMP and nNMQ are right
1. Given
2. ?
3.
4.
5.
6.
7.
triangles.
Point M is the midpoint of }
LN.
?
nPMQ is an isosceles triangle.
?
nLMP > nNMQ
M
N
P
P
3. ?
4. Definition of midpoint
5. Given
6. Definition of isosceles triangle
7. ?
GPSQSPCMFNTPMWJOHIFMQBUDMBTT[POFDPN
PROOF In Exercises 35 and 36, write a proof.
35. GIVEN c }
PQ bisects ∠ SPT, }
SP > }
TP
PROVE
c nSPQ > nTPQ
36. GIVEN c }
VX > }
XY, }
XW > }
YZ , }
XW i }
YZ
PROVE
V
P
S
c nVXW > nXYZ
T
X
P
Y
W
Z
4.4 Prove Triangles Congruent by SAS and HL
245

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