Triangle Congruency Properties

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Triangle Congruency Properties
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One pair of congruent sides or congruent angles
does not mean congruent
One pair of congruent angles
One pair of congruent sides
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Two pairs of congruent sides or congruent angles
does not mean congruent
Two pairs of congruent angles
Two pairs of congruent sides
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What Is Triangle Congruency?
By definition, if three sides and three angles of
one triangle are congruent to three sides and
three angles of a second triangle, then the
triangles are congruent.
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Six different combinations
AAS
SAS
AAA
ASA
SSS
SSA
Click on each combination to explore it more
Once youve read about each combination, click
the star
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SSS
side-side-side
1) Draw three line segments on your paper 2)
Label them AB, BC, and CA 3) Construct two
separate triangles using these line segments
A
B
B
C
A
C
What do you notice about your two triangles?
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SSS
If three sides of one triangle are congruent to
three sides of a second triangle, the two
triangles are congruent.
Explore other combinations
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ASA
angle-side-angle
1) Draw two angles and one line segment on your
paper 2) Label them AB, g A, and g B 3) Construct
two separate triangles using these line segments
and angle
A
B
A
B
What do you notice about your two triangles?
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ASA
If two angles and the included side of one
triangle are congruent to two angles and the
included side of another triangle, the triangles
are congruent.
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AAS
angle-angle-side
1) Draw two angles and one line segment on your
paper 2) Label them AC, g A, and g B 3) Construct
two separate triangles using this line segment
and angles
C
A
A
B
What do you notice about your two triangles?
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AAS
If two angles and a non included side of one
triangle are congruent to two angles and the
corresponding non-included side of another
triangle, the two triangles are congruent.
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SAS
side-angle-side
1) Draw one angle and two line segments on your
paper 2) Label them AB, g A, and AC. 3) Construct
two separate triangles using these line segments
and angle
C
A
A
A
B
What do you notice about your two triangles?
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SAS
If two sides and the included angle are congruent
to two sides and the included angle of a second
triangle, the two triangles are congruent.
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SSA
side-side-angle
1) Draw one angle and two line segments on your
paper 2) Label them AC, BC, and g A. 3) Construct
two separate triangles using these line segments
and angle
C
C
A
A
B
What do you notice about your two triangles? Can
they be drawn differently?
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SSA
Two triangles with two sides and a non-included
angle equal may or may not be congruent.
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AAA
angle-angle-angle
1) Draw three angles on your paper (whose total
degrees equals 180) 2) Label them g A, g B, and g
C. 3) Construct two separate triangles using
these angles
C
A
B
What do you notice about your two triangles?
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AAA
If two angles on one triangle are equal to two
angles on another triangle, then the triangles
are similar, but not necessarily congruent.
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Quiz
Click on the set of triangles that are congruent
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Quiz
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Some additional sites with valuable information
Wikipedia Triangle Congruence
Mr. Coxs homepage
Triangle Congruency Applets