## Tuesday, November 23, 2021

### Geometry Problems of the Day (Geometry Regents, January 2012)

Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones.

More Regents problems.

### Geometry Regents, January 2012

Part IV: Each correct answer will receive 6 credits. Partial credit is available.

38. In the diagram below of quadrilateral ABCD,AD ≅ BC and ∠DAE ≅ ∠BCE.

Line segments AC, DB, and FG intersect at E.

Prove: Triangle AEF ≅ triangle CEG

There is enough here to show that ABCD is a parallelogram, if that becomes important. There are properties that could be used, the most important of which is probably that the diagonals will bisect each other.

You are given a pair of congruent angles. You have a pair of vertical angles. You can show that the contained sides are parallel. So you can prove congruency through ASA.

This is not an obvious one. But then again, it's a Part IV problem.

 Statement Reason 1. AD ≅ BC, ∠DAE ≅ ∠BCE Given 2. AD || BC Alternate interior angles are congruent 3. ABCD is a parallelogram A quadrilateral with one pair of sides that are both parallel and congruent is a parallelogram 4. AE ≅ CE The diagonals of a parallelogram bisect each other 5. ∠AEF ≅ &∠CEG Vertical angles are congruent 5. Triangle AEF ≅ triangle CEG ASA

End of Exam.

More to come. Comments and questions welcome.

More Regents problems.

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