Two or more angles are said to be supplementary if and only if they add up to [tex]180^{o}[/tex].
Thus the required statements and appropriate reasons are stated below:
Two lines are said to be perpendicular when the measure of the angle between them is a right angle. Thus all right angle is congruent.
Angles are said to be congruent if and only if they have equal measure.
Thus in the given question, it can be deduced that:
STATEMENT REASONS
1. AC ⊥ BD, <1 ≅ <4 Given
2. <BCA = [tex]90^{o}[/tex], <DCA = [tex]90^{o}[/tex] Definition of perpendicular lines
3. <BCA ≅ <DCA Right angles are congruent
4. <BCA = <1 + <2 Angle addition property
5. <DCA = <3 + <4 Angle addition property
6. <1 + <2 = <3 + <4 Distributive property
7. <1 + <2 = <4 + <3 Substitution property
8. <2 ≅ <3 Reflexive property
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