The SSS congruency theorem provides a sound basis for concluding that triangle ABC is congruent to triangle CDA, affirming the relationship between the sides of the two triangles within the context of the parallelogram.
The given information establishes that a parallelogram has opposite sides of equal length, specifically stating that side AB is congruent to side CD, side BC is congruent to side DA, and side AC is congruent to side CA. The goal is to prove the congruence between triangle ABC and triangle CDA using the Side-Side-Side (SSS) congruency theorem.
In a parallelogram, opposite sides are not only equal but also parallel. This property allows for the formation of two triangles, namely triangle ABC and triangle CDA. The SSS congruency theorem asserts that if the corresponding sides of two triangles are equal, then the triangles themselves are congruent.
By applying the SSS rule, we can establish the congruence between triangle ABC and triangle CDA based on the given information. The three corresponding sides AB, BC, and AC of triangle ABC are congruent to the corresponding sides CD, DA, and CA of triangle CDA, respectively.
The question probable may be:
What is the missing reason in the proof?
Statements
Reasons
1. AB / CD; BC // DA 1. given
2. Quadrilateral ABCD 2. definition of parallelogram
is a
3. AB CD; BC = DA 3. opposite sides of a
parallelogram are >
4. AC AC
4. reflexive property
5. AABC 2 ACDA 5. ?
perpendicular bisector theorem
Pythagorean theorem
HL theorem
SSS congruence theorem