Answer: B) Angle-Side-Angle
This abbreviates to ASA.
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Explanation:
We're told that segment AC bisects angle DAB. This means angle DAB is cut into two equal halves. Those two smaller equal angles are angle DAC and angle CAB. So we can say angle DAC = angle CAB.
Also, we're told that segment AC bisects angle DCB. This means angle DCA = angle ACB
Lastly, through the reflexive property, we know that AC = AC. Any segment is congruent to itself.
These three facts allow use to use ASA. Note how the congruent sides are between the congruent angles mentioned. With ASA, the "S" is between the "A"s to reflect this.
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We can break things down like this:
- A: angle DAC = angle CAB
- S: segment AC = segment AC
- A: angle DCA = angle ACB
The order matters and ASA is slightly different from AAS. In the case of AAS, the side is not between the angles.
