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Latest
news bulletin:
The
most popular congruent figures are triangles!
Be
sure to remember that in congruent figures, the corresponding parts are also
congruent. |
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When
two triangles are congruent, there are 6 facts that are
true about the triangles:
- there are
3 sets of
congruent (equal) sides
and
- there are
3 sets of
congruent (equal) angles.
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NOTE:
The corresponding congruent sides are marked with small
straight line segments called hash
marks.
The corresponding congruent angles are marked with arcs. |
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| The 6 facts
of congruent triangles:
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Note:
The order of the letters in the
names of the triangles displays the corresponding relationships.
Even without the picture, you would know that <A would be congruent to
<D, and segment BC would be congruent to segment EF, because they are in
the same position in each triangle name.
Wow!
Six facts for every set of congruent triangles!
Fortunately, when
we need to PROVE (or show) that triangles are congruent, we do NOT need
to show all six facts are true. There are certain combinations of the
facts that are sufficient to prove that triangles are congruent.
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Methods
of Proving (Showing) Triangles to be Congruent |
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SSS |
If
three sides of one triangle are congruent to three sides
of another triangle, the triangles are congruent. |
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SAS |
If two sides
and the included angle of one triangle are congruent to
the corresponding parts of another triangle, the
triangles are congruent. |
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ASA |
If
two angles and the included side of one triangle are
congruent to the corresponding parts of another
triangle, the triangles are congruent. |
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AAS |
If two angles
and the non-included side of one triangle are congruent
to the corresponding parts of another triangle, the
triangles are congruent. |
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HL |
If
the hypotenuse and leg of one right triangle are
congruent to the corresponding parts of another right triangle, the
right triangles are congruent. |
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BE
CAREFUL!!!
Only the combinations listed above work.
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AAA
works fine to show that triangles are the same SHAPE
(similar), but does NOT
work to show congruent!
You can
draw 2 equilateral triangles that are the same shape but
not the same size. |
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ASS
is referred to as the Donkey Theorem.
It
does NOT
work!!! |
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