SOLUTION: hi im having some trouble with helping my sister with her math homework.. her name is kelly and shes in geometry in middle school. She is currently studying medians altitudes, and

Algebra ->  Geometry-proofs -> SOLUTION: hi im having some trouble with helping my sister with her math homework.. her name is kelly and shes in geometry in middle school. She is currently studying medians altitudes, and       Log On


   

Question 377787: hi im having some trouble with helping my sister with her math homework.. her name is kelly and shes in geometry in middle school. She is currently studying medians altitudes, and perpendicular bisectors...
The problem that we need help on is
IF THE POINT LIES ON THE PERPENDICULAR BISECTOR OF A SEGMENT, THEN THE POINT IS EQUIDISTANT FROM THE ENDPOINTS OF THE SEGMENT

GIVEN: LINE l IS THE PERPENDICULAR BISECTOR OF SEGMENT BC; A IS ON l
PROVE THAT AB IS EQUAL TO AC
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
here's the strategy
you can fill in all the little details for a "formal" proof

let M be the point of intersection of BC and the bisector

BM equals MC ___ definition of bisector (given)

angle BMA equals (congruent) angle CMA ___ right angles formed by the perpendicular are equal
(perpendicular is given)

AM equals AM (itself) ___ reflection identity

so triangle BMA equals (congruent) triangle CMA ___ SAS

AB equals (congruent) AC ___ Corresponding Parts of Congruent Triangles are Congruent