Answered

IDNLearn.com provides a comprehensive solution for all your question and answer needs. Ask any question and get a detailed, reliable answer from our community of experts.

How do I prove HM = KM, if GJ is the perpendicular bisector of HK?

How Do I Prove HM KM If GJ Is The Perpendicular Bisector Of HK class=

Sagot :

Answer:

Step-by-step explanation:

Since GJ is the perpendicular bisector of HK it bisects HK and make J the midpoint of HK. Since J  is the midpoint we can construct a congruence statement of  KJ≅JH. Then we know in the diagram Angle MJK= 90°, becuase it form a ⊥ line so it is 90° that also means MHJ forms a 90 ° angles becuase they also form a ⊥ line. So that means KJM≅HJM because of transitive property(a=b, b=c, then a=c). Both triangles also include side MJ, so using the reflexitive property( a=a),They are congruent. Since we proved they have a two congruent sides, with a included angle in between them we can use the SAS theorem (Side-Angle-Side) to prove they are congruent. So ΔKMJ≅ΔHMJ Then KM=HM by CPCTC.

Your presence in our community is highly appreciated. Keep sharing your insights and solutions. Together, we can build a rich and valuable knowledge resource for everyone. IDNLearn.com is committed to your satisfaction. Thank you for visiting, and see you next time for more helpful answers.