SOLUTION: I have a confusing proof. GIVEN: 1)triangle ABC is isosceles. 2)line segment BD is a median to base AC PROVE: line segment BD is also an altitude

Algebra ->  Geometry-proofs -> SOLUTION: I have a confusing proof. GIVEN: 1)triangle ABC is isosceles. 2)line segment BD is a median to base AC PROVE: line segment BD is also an altitude       Log On


   

Question 246288: I have a confusing proof.
GIVEN: 1)triangle ABC is isosceles.
2)line segment BD is a median to base AC
PROVE: line segment BD is also an altitude
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
Triangle is ABC.

AD intersects AC at D.

It's a median so it splits the line AC into 2 equal parts.

You have:

AB = BC (legs of isosoceles triangle)
AD = DC (median splits AC into 2 equal parts by definition)

BD = BD (identity - same line segment is equal to itself)

triangles ABD and DBC are congruent (sss)

angle ADB = angle CDB (corresponding angles of congruent triangles are equal).

angle ADB and CDB are supplementary (their sum is equal to 180 degrees because their outer line segments form a straight line).

angle ADB and angle CDB must each be 90 degrees (they are equal and their sum is equal to 180.).

angle ADB and angle CDB are right angles (right angle = 90 degrees).

BD is perpendicular to AC (intersects at a right angle therefore is perpendicular).

or something like that.

you prove the angles are congruent.

you prove the angles have to be right angles.

that proves that the median is also an altitude because an altitude is perpendicular to the base by definition.