http://www.ck12.org Chapter 4. Triangles and Congruence
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a. Yes, 4 CAD∼= 4 ACBbecause^6 CAD∼=^6 ACBand^6 BAC∼=^6 ACDby Alternate Interior Angles.AC∼=AC
by the Reflexive PoC and^6 ADC∼=^6 ABCby the 3rdAngle Theorem.
b. At this point in time, we do not have enough information to show that the two triangles are congruent.
We know thatAB∼=BCandDB∼=BEfrom the definition of a midpoint. By vertical angles, we know
that^6 DBC∼=^6 ABE. This is only two sides and one pair of angles; not enough info, yet.- We need to know three pairs of congruent sides and two pairs of congruent angles. From this, we can assume
the third pair of angles are congruent from the 3rdAngle Theorem.