3. When triangles are congruent,
one triangle can be moved
(through one, or more, rigid
motions) to coincide with the
other triangle. All corresponding
sides and angles will be
congruent.
9. 1. Start by marking
the given
information on
your diagram
(using hash marks,
arcs, etc.).
Tips for Preparing
Congruent Triangle Proofs:
2. Remember your
definitions! If the
given information
contains definitions,
be sure to use them
as they are "hints" to
the solution.
9
10. 3. Look for any parts
that your triangles
may "share". These
common parts will
automatically be one
set of congruent
parts.
Tips for Preparing
Congruent Triangle Proofs:
4. Examine the
diagram to see
what else you may
already know
about the figure.
10
11. 5. If you are trying to
prove specific "parts"
of the triangles, find a
set of triangles that
contains these parts
and prove those
triangles congruent.
Tips for Preparing
Congruent Triangle Proofs:
6. If the triangles you
need are
overlapping, try
drawing the two
triangles separately.
It may give you a
better look at the
known information.
11
12. 7. Keep in mind that there may be more than
one way to solve the problem.
Tips for Preparing
Congruent Triangle Proofs:
12
13. A PROOF IS A PUZZLE TO
BE SOLVED! A proof is like a big
"puzzle" waiting to
be solved. Look
carefully at the
"puzzle" and use all
of your geometrical
strategies to arrive
at a solution.
13
14. Some of the more common theorems,
properties, and definitions used with
congruent triangles:
14
15. Some of the more common theorems,
properties, and definitions used with
congruent triangles:
15
27. ACTIVITY 2: FILL ME UP!
Directions: Fill in the blanks. Use the
words inside the box to complete the
statements and reasons in proving
the triangle congruence.
The good news is that when proving triangles congruent, it is not necessary to prove all six facts to show congruency. There are certain ordered combinations of these facts that are sufficient to prove triangles congruent. These combinations guarantee that, given these facts, it will be possible to draw triangles which will take on only one shape (be unique), thus insuring congruency.
When working with congruent triangles, remember to:
When working with congruent triangles, remember to:
When working with congruent triangles, remember to:
When working with congruent triangles, remember to:
Notice that there seems to be missing information. You are expected to "find" the additional information by observing the vertical angles at C. (Use SAS for this example.)
Notice that there seems to be missing information. You are expected to "find" the additional information by observing the vertical angles at C. (Use SAS for this example.)
Notice that there seems to be missing information. You are expected to "find" the additional information by observing the vertical angles at C. (Use SAS for this example.)
Notice that there seems to be missing information. You are expected to "find" the additional information by observing the vertical angles at C. (Use SAS for this example.)
