CK-12 Geometry-Concepts

http://www.ck12.org Chapter 4. Triangles and Congruence

Answers:

1. We can see from the markings that^6 B∼=^6 C,^6 A∼=^6 D, and^6 AEB∼=^6 DECbecause they are vertical angles.
   Also, we know thatBA∼=CD,EA∼=ED, andBE∼=CE. Because three pairs of sides and three pairs of angles are
   all congruent and they are corresponding parts, this means that the two triangles are congruent.


2. While there are congruent corresponding parts, there are only two pairs of congruent sides, the marked ones and
   the shared side. Without knowing whether or not the third pair of sides is congruent we cannot say if the triangles are
   congruent using the definition of congruent triangles. Note, this does not mean that the triangles arenot congruent,
   it just means that we need more information in order to say they are congruent using thedefinition of congruent
   triangles(congruent triangles have three pairs of congruent angles and three pairs of congruent sides).


3. We can see from the markings that^6 G∼=^6 L,^6 F∼=^6 K, and therefore^6 H∼=^6 Mby the Third Angle Theorem.
   Also, we know thatMK∼=F H,GF∼=LK, andGH∼=LM. Because three pairs of sides and three pairs of angles are
   all congruent and they are corresponding parts, this means that the two triangles are congruent.

Explore More

The following illustrations show two parallel lines cut by a transversal. Are the triangles formed definitively
congruent?

1.

2.