Download 4.3: Analyzing Triangle Congruence

4.3: Analyzing Triangle
Congruence
Expectations:
G2.3.1: Prove that triangles are congruent
using the SSS, SAS, ASA, and AAS criteria
and that right triangles are congruent using
the hypotenuse-leg criterion.
G2.3.2:Use theorems about congruent
triangles to prove additional theorems and
solve problems, with and without use of
coordinates.
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4.3: Analyzing Triangle Congruence
AAA Conjecture
a. Draw a 30°, 60°, 90 right
triangle.
b. Compare your triangle to a
neighbor’s.
c. What can be said about the
triangles?
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4.3: Analyzing Triangle Congruence
AAA Conjecture
AAA is not sufficient to conclude
triangles are congruent.
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4.3: Analyzing Triangle Congruence
SSA Conjecture
a. Draw a triangle with 2 sides that are
8cm and 6 cm, with a non-included
angle of 40.
b. Compare your triangle to a
neighbor’s.
c. What can be said about the
triangles?
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4.3: Analyzing Triangle Congruence
SSA Conjecture
SSA is not sufficient to prove triangles
are congruent.
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4.3: Analyzing Triangle Congruence
SsA
A very special case of SSA is valid for
proving triangles congruent. It is
referred to as SsA. In SsA, the angles
given must be opposite the longer of
the 2 sides.
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4.3: Analyzing Triangle Congruence
SsA
E
B
F
C
A
D
Given the above information, ΔABC  ΔDEF.
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4.3: Analyzing Triangle Congruence
SsA
In two triangles, if two sides of the first
are congruent to two sides of the
second and the angle opposite the
longer of the two sides of the first is
congruent to the corresponding angle
of the second triangle, then the
triangles are congruent.
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4.3: Analyzing Triangle Congruence
Are the triangles congruent?
Justify your answer.
Z
C
10 in
50º
A
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10 in
60º
50º
B
60º
X
4.3: Analyzing Triangle Congruence
Y
Non-Included Sides
AC is a
nonincluded
side for A
and B
C
BC is a
nonincluded
side for A
and B
B
A
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4.3: Analyzing Triangle Congruence
AAS Congruence Theorem
If two angles and a non-included side
of one triangle are congruent to two
angles and the corresponding nonincluded side of the second triangle,
then the triangles are congruent.
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4.3: Analyzing Triangle Congruence
HL Congruence Theorem
In 2 right triangles, if the hypotenuse
and a leg of the first are congruent to
the hypotenuse and a leg of the
second, then the triangles are
congruent.
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4.3: Analyzing Triangle Congruence
Prove the HL Congruence
Theorem
F
C
A
B
D
E
Given: AC = DF and BC = EF
Prove: ABCDEF
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4.3: Analyzing Triangle Congruence
Assignment
pages 231-234,
# 10-18 (evens), 20-29 (all), 30, 32, 34,
35, 37, 42, 43
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4.3: Analyzing Triangle Congruence