501 Geometry Questions

Some Congruency Basics

When items are congruentit means they are identical. In order to indicate
congruence, the following symbol is used:. Therefore, ΔAΔB, is read,
“triangle A is congruent to triangle B.”

Congruent line segmentsare line segments that have the same length,
regardless of how they are oriented on paper.

Congruent anglesare angles that have the same measurement in degrees.
Since they do not need to open or face the same direction, sometimes they
can be difficult to identify. Congruent angles are shown with a small arc
and an identical number of hash marks. In the following illustration, ∠XYZ
∠ABC even though they are facing different directions.

Naming congruent figures accuratelytakes careful consideration. Look-
ing at the following figure, you might remember that it does not matter if
we refer to ΔABC asΔBCA or asΔCAB since orderand directionare unim-
portant when naminga single triangle. However, when discussing congru-
ent figures, the order of vertexes from one figure must correspond with the
congruent vertexes from the other figure. For example, if we were to use
ΔABC, then we would need to start the name of the second triangle with
the smallest angle Q, and follow it with the largest angle R, and end with
the middle angle S. Therefore, ΔABCΔQRS. It would be incorrectto
write ΔABCΔQSR because that implies thatB is congruent toS, but
these angles are not congruent.

Y

X ∠XYZ ≅ ∠ABC : ∠XYZ is congruent to ∠ABC

Z

A

B

C

501 Geometry Questions