Proving the Single Opposite Side Pair Theorem Given: AD=BC and AD BC prove:ABCD is a parallelogram
Answers
Answer:
8 parts
Step-by-step explanation:
1. AD≅BC Given
2. AD║BC Given
3. ∠DAC and ∠BCA Def. of alt.
are alt. interior angles interior angle
4. ∠DAC ≅ ∠BCA alternate interior angle theorem
5. AC ≅ AC reflexive property
6. ΔDAC ≅ ΔBCA SAS
7. AB ≅ CD CPCTC
8. ABCD is a parallelogram parallelogram side theorem
The proof of ABCD is a parallelogram is given in the solution.
What is a parallelogram?In geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
The proof is as follows :-
AD≅BC (Given)
AD║BC (Given)
∠DAC and ∠BCA (alternate angles)
∠DAC ≅ ∠BCA (alternate angle)
AC ≅ AC (common)
ΔDAC ≅ ΔBCA (SAS rule)
AB ≅ CD (CPCT)
Hence,
ABCD is a parallelogram (by the definition of parallelogram)
Hence, proved.
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