Prove that,in an isosceles triangle,the bisector of the vertical angle

1.	Prove that,in an isosceles triangle,the bisector of the vertical angle,the altitude from the vertex and the median to the base are coincident.
Answer» Answer: Proof: Consider the two triangles ABD and ACD, AB = AC (Given) Angle BAD = Angle CAD (since given AD bisects angle BAC) AD = AD (Common sides) Thus the two triangles ABD and ACD are consistent (By 'SAS' compatibility adage of triangles) therefore angle ADB = edge ADC - (1) (Corresponding parts of CONGRUENCE triangles are equivalent) In any case, these two are direct PAIR that is their entirety is 180 degrees - (2) Thus from (1) and (2), EVERY one of the points ADB and ADC are 90 degrees. Therefore, AD is perpendicular to BC.

Prove that,in an isosceles triangle,the bisector of the vertical angle,the altitude from the vertex and the median to the base are coincident.

Answer»

Answer:

Proof:

Consider the two triangles ABD and ACD,

AB = AC (Given)

Angle BAD = Angle CAD (since given AD bisects angle BAC)

AD = AD (Common sides)

Thus the two triangles ABD and ACD are consistent (By 'SAS' compatibility adage of triangles)

therefore angle ADB = edge ADC - (1) (Corresponding parts of

CONGRUENCE triangles are equivalent)

In any case, these two are direct PAIR that is their entirety is 180 degrees - (2)

Thus from (1) and (2), EVERY one of the points ADB and ADC are 90 degrees.

Therefore, AD is perpendicular to BC.

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