Question

segment ac is on the line of reflection, so it is taken to itself, making segment ac congruent to segment ac.
segment ab reflects to segment dropdown, and segment cd is a reflection of segment dropdown, making each pair congruent.
angle dac is a reflection of angle dropdown, angle acb reflects to angle dropdown, and angles abc and dropdown coincide, making each pair of angles congruent.
with all corresponding parts shown to be congruent, it follows that triangle abc is congruent to triangle adc.

Explanation:

Step1: Recall Reflection Properties

In a reflection, corresponding segments and angles are congruent. For triangle \(ABC\) and \(ADC\) with line of reflection \(AC\):

• Segment \(AB\) should reflect to \(AD\) (since \(A\) is on the line of reflection, \(B\) reflects to \(D\)).
• Segment \(CD\) is the reflection of \(CB\) ( \(C\) is on the line, \(D\) reflects to \(B\) or vice - versa).
• Angle \(DAC\) is the reflection of angle \(BAC\) ( \(A\) is on the line, \(D\) reflects to \(B\), so \(\angle DAC\) and \(\angle BAC\) are corresponding).
• Angle \(ACB\) reflects to angle \(ACD\) ( \(C\) is on the line, \(B\) reflects to \(D\), so \(\angle ACB\) and \(\angle ACD\) are corresponding).
• Angles \(ABC\) and \(ADC\) coincide (since \(B\) reflects to \(D\) and \(A,C\) are on the line, \(\angle ABC\) and \(\angle ADC\) are corresponding).

Step2: Fill in the Blanks

1. Segment \(AB\) reflects to segment \(AD\).
2. Segment \(CD\) is a reflection of segment \(CB\).
3. Angle \(DAC\) is a reflection of angle \(BAC\).
4. Angle \(ACB\) reflects to angle \(ACD\).
5. Angles \(ABC\) and \(ADC\) coincide.

Answer:

• Segment \(AB\) reflects to segment \(\boldsymbol{AD}\)
• Segment \(CD\) is a reflection of segment \(\boldsymbol{CB}\)
• Angle \(DAC\) is a reflection of angle \(\boldsymbol{BAC}\)
• Angle \(ACB\) reflects to angle \(\boldsymbol{ACD}\)
• Angles \(ABC\) and \(\boldsymbol{ADC}\) coincide