The water under a draw bridge was 15 feet deep at midnight. As the tide went out, the
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Answer:
From the graph attached, we know that by the corresponding angle theorem, this theorem is about all angles that derive form the intersection of one transversal line with a pair of parallels. Specifically, corresponding angles are those which are placed at the same side of the transversal, one interior to parallels, one exterior to parallels, like
and
.
We also know that, by definition of linear pair postulate, and
are linear pair. Linear pair postulate is a math concept that defines two angles that are adjacent and for a straight angle, which is equal to 180°.
They are supplementary by the definition of supplementary angles. This definition states that angles which sum 180° are supplementary, and we found that and
together are 180°, because they are on a straight angle. That is,
If we substitute for
, we have
, which means that
and
are also supplementary by definition.
Answer:
To Prove: Quadrilateral ABCD is a parallelogram.
Proof: In Δ ABE and ΔCDE
1. AE = EC and BE = ED [ Diagonals bisect each other]
2.∠ AEB = ∠ CED [ vertically opposite angles]
Δ ABE ≅ ΔCDE---------- [SAS]
∠ ACD ≅ ∠CAB [Corresponding angles of congruent triangles are congruent⇒This statement is untrue ∴ these are alternate interior angles not corresponding angles.]
6. The converse of alternate interior interior angle theorem states that if two parallel lines are cut by a transversal then alternate interior angles are equal.
7. In ΔBEC and ΔAED
∠BEC = ∠AED [ Vertical Angles Theorem ]
AE = EC and BE = ED [ Diagonals bisect each other]
⇒ ΔBEC≅ ΔDEA [ SAS criterion for congruence]
9. DBC ≅ BDA [ Corresponding angles of congruent triangles are congruent⇒This statement is untrue ∴ these are alternate interior angles not corresponding angles.]
As pair of triangles are congruent ∵ quadrilateral ABCD is a parallelogram.
Step 3 is m∠AEB = m∠CED
These pair of angles are vertically opposite angles of ΔAEB and ΔCED.
Option [D. Vertical Angles Theorem] is correct.
