1)
S: angles 1 & 2 are supplementary.
R: Deffinition of supplementary angles.
S: angles 1 & 4 are congruent.
R: Deffinition of corresponding angles.
S: Angles 4 & 5 are supplementary.
R: Deffinition of supplementary angles.
S: Angles 1 & 5 are supplementary.
R: Transitivity.
2)
We will have the following:
S: angle BAC congruent with angle DCA.
R: Given.
S: Segment BC congruent with segment AD.
R: Sides that are opposite to congruent angles are congruent.
S: AC is a common side.
R: Given in the problem.
S: Triangles ABC and CAD are congruent by SAS.
R: Segmenst BC & AC are corresponding, angles BAC & DCA are congruent and segment AC is common.
S: Segment BD will be a common side to triangles ABD & CDB.
R: Given in the problem.
S: Triangles ABD & CDB are congruent.
R: Angles BAD & DCB are congruent (Proven previously implicitly), and angles ABC & CDA are congruent (Proven previously implicitly) and segment BD is common, also segments AB and CD are congruent (Proven previously implicitly).
S: Angles ABD & CDB are congruent.
R: Transitivity.
3)
S: mR: Given.
S: R: Angles opposite by the vertex.
S: mR: Deffinition of congruent angles.
S: mR: Deffinition of congruent angles.
S: 78° + 102° = 180°.
R: Addition property of equality.
S: mR: Deffinition of supplementary angles.
S: mR: Deffinition of supplementary angles.
S: m || n.
R: Property of transitivity.