Congruency of Triangles
Get College Mathematics Help, Mathematics Exam Preparation & AP Mathematics Tutoring
 |
Congruency of Triangles |
 |
| |
Congruent triangles have the same size and the same shape. The corresponding sides and the
corresponding angles of congruent triangles are equal.
Δ ABC and ΔDEF have the same size and shape. In fact, if you could 'pick up' Δ ABC you could fit it
exactly over ΔDEF so that the vertices and sides coincide. Of course, you would have to put C on top
of F, A on D and B on E, because they wouldn't match any other way. We convey all this information
by saying that Δ ABC is congruent to ? DEF.
In symbolic form, we write this as ? ABC =~ ? DEF.
(The congruent to symbol looks like an equals
sign but with three instead of two horizontal lines).
Note: The order of the points in the names of the
?s is important. Δ ABC is congruent to
Δ DEF
says that the triangles will coincide when A is placed on D, B on E, and C on F. (We would not say
that Δ ABC is congruent to ? EFD in the above).
The congruent triangles ABC and DEF have equal
corresponding sides (AB = DE, BC = EF, CA = FD)
and equal corresponding angles .
Side-Angle-Side (SAS) congruence rule:
Two triangles are congruent if two sides and the
included angle of one triangle are equal to the sides and the included angle of
the other triangle.
Segment PQ is congruent to segment ST because
PQ = ST = 4. Angle Q is congruent to angle
T
because  Q = T = 100 degrees. Segment QR is congruent to segment
TV because QR = TV
= 5.
Triangle PQR is congruent to ? STV
by Side-Angle-Side.
|
|
 |
|
 |
Submit your homework or assignment.
