Geometry: Common Core (15th Edition)

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

Chapter 4 - Congruent Triangles - 4-4 Using Corresponding Parts of Congruent Triangles - Practice and Problem-Solving Exercises - Page 247: 16

Answer

△PCA and △PCB are congruent because of ASA. PA = PB since corresponding parts of a congruent triangle are congruent.

Work Step by Step

Proof: ℓ is perpendicular to AB - given ℓ bisects AB at C - given AC ≅ CB - definition of bisect, both lengths are equal ∠ACP ≅ ∠BCP - definition of perpendicular, both angles are 90 degrees PC ≅ PC - Reflexive Property of Congruence △PCA ≅ △PCB - Postulate 4-3 Angle-Side-Angle (ASA) Postulate PA = PB - Corresponding parts of ≅ △ are ≅
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