Given that the opposite sides of a parallelogram are congruent, a diagonal
of the parallelogram forms two congruent triangles.
The correct options to complete the proof are;
- <u>Opposite sides of a parallelogram;</u> ABCD is a parallelogram
- <u>Reflexive property of congruency</u>
Reasons:
The completed two column proof is presented as follows;
Statement Reason
1. ABCD is a parallelogram 1. Given
2. ≅ and ≅ 2. <u>Opposite sides of a parallelogram</u>
3. ≅ 3. <u>Reflexive property of congruency</u>
4. ΔABC ≅ ΔCDA 4. <u>SSS</u>
The correct options are therefore;
<u>Opposite sides of a parallelogram;</u> ABCD is a parallelogram
Reflexive property of congruency
SSS;
Reason 2. Opposite sides of a parallelogram, which is based on the
properties of a parallelogram and that ABCD is a parallelogram.
Reason 3. The reflexive property of congruency, states that a side is
congruent to itself.
Reason 4. SSS is an acronym for Side-Side-Side, which is a congruency
postulate that states that if the three sides of one triangle are equal to the
three sides of another triangle, then the two triangles are congruent.
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