SOLUTION: Given: Segment CS and segment AT are altitudes; Segment CS is congruent to segment AT Prove: Segment AS is congruent to segment CT Use this diagram to help you: http://i164.ph

Algebra ->  Geometry-proofs -> SOLUTION: Given: Segment CS and segment AT are altitudes; Segment CS is congruent to segment AT Prove: Segment AS is congruent to segment CT Use this diagram to help you: http://i164.ph      Log On


   

Question 173265: Given: Segment CS and segment AT are altitudes; Segment CS is congruent to segment AT
Prove: Segment AS is congruent to segment CT
Use this diagram to help you:
http://i164.photobucket.com/albums/u27/foxymccloud/geometry.jpg
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

    Statement                                      Reason
-----------------------------------------------------------------------

1.  Angle ASC is right angle                       Definition of Altitude (given) 


2.  Angle ATC is right angle                       Definition of Altitude (given)


3.  Angle ATC = Angle ASC                          Right Angle Theorem


4.  CS = AT                                        Given


5.  AC = AC                                        Reflexive Property of Congruence


6.  triangle ASC = triangle ATC                    SAS Postulate


7.  AS = CT                                        CPCTC



Notes:

# 1 Remember, an altitude is a segment that runs from one vertex to the opposite side (and forms a 90 degree angle with the opposite side).

# 2 The Right Angle Theorem states that all right angles are congruent.

# 3 CPCTC = Corresponding parts of congruent triangles are congruent.