Chapter 4.2, Problem 16WE

To determine

To find: the missing reasons from the prove $\Delta ABC\cong \Delta CDA$ .

Explanation of Solution

Given information:

Given figure,

Given:

  $\overline{AB}\parallel \overline{DC};\overline{AB}\cong \overline{DC}$

Calculation:

SSS Postulate: if there sides of triangle are equal to the three corresponding sides of another triangle, then the triangles are congruent.

SAS Postulate: If two sides and the angle included between them of triangle are equal to the two corresponding sides and the angle included between them of another triangle, then the triangles are congruent.

ASA Postulate: If two angles and the included side of triangle are equal to the two corresponding angles and the included sides of another triangle, then the triangles are congruent.

Given:

  $\overline{AB}\parallel \overline{DC};\overline{AB}\cong \overline{DC}$

Prove: $\Delta ABC\cong \Delta CDA$

Proof:

  $\overline{AB}\cong \overline{DC}$

Reason 1: Given

  $\overline{AC}\cong \overline{DC}$

Reason 2: Reflexive property

  $\overline{AB}\parallel \overline{DC}$

Reason 3: Given

  $\angle BAC\cong \angle DCA$

Reason 4: Alternate interior angles

  $\Delta ABC\cong \Delta CDA$

Reason 5: SAS Postulate.