Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 4 - Congruent Triangles - Mid-Chapter Quiz: 14

Answer

Congruent by ASA.

Work Step by Step

We see that angles H and K are alternate interior angles since HL and KJ are marked as congruent. Thus, they are congruent by the alternate interior angles theorem. We also see that angle HNL is congruent to KNJ. After all, the two angles form vertical angles. So, the two angles are congruent by the vertical angles theorem. Now, we have established that there are two congruent angles and one congruent side. The congruent side falls between the two pairs of congruent angles, so we see that the triangles are congruent by the ASA postulate.
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