Download Congruent Triangles

Congruent Triangles
Featuring SSS and SAS (side-side-side and side-angle-side)
Congruent Triangles
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We know that in order for polygons to be congruent all parts of the
first polygon must be congruent with all the corresponding parts of
the second polygon.

All sides must be congruent
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All angles must be congruent

For triangles we have three sides and three angles, so there are six
items that have to be congruent.

Remember: the order of the letters used for sides and angles is
extremely important! Each side and angle designation MUST match
the corresponding side or angle.
Congruent Triangles
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The example below note how the letters are ordered in the congruency
relation. ABCD ≅ EFGH
Congruent Triangles

If the polygons to the right are congruent (HIJK ≅
LMNO), what are the corresponding parts that are
congruent?

Sides:

Angles:
Congruent Triangles


Figures (drawings of polygons) can be translated, rotated and reflected
without losing congruency. That means that two polygons might look
different because they have been flipped over, turned around or moved.
However, as long as the corresponding parts are congruent, the polygons are
still congruent!
We can also use these transformations to prove that two figures are
congruent by moving one object until it overlays (matches) the other
polygon.
Your turn!

Work with a partner to determine whether
triangles to the right are congruent. Does it matter
if we break apart the triangles?

Answer: triangle ABC ≅ EDC
 Work with a partner to determine whether
triangles to the right are congruent. Note: 𝐵𝐷
is a perpendicular bisector of 𝐴𝐶.
 Answer: triangle ABD ≅ CBD
The Third Angle Theorem

If two angles of a triangle are congruent with two angles from a second
triangle then the third angle in each triangle must be congruent. (Note
this can be proven in a proof very much like the one we used to show
that three angles of a triangle must add up to 180 degrees.)
Proofs with congruent triangles
Let’s say that we wanted to prove that two triangles are congruent by
using a formal proof. Here’s one way in which we might do that.