Question

State the given and the conclusion.
Write the proof.
~iF a line segments bisects an angle of a triangle and is also perpendicular to the base, then the triangle is isosceles.

Answer 1

@aum

Answer 2

Obviously the line that bisects the angle divides the triangle into to two triangle.

What is true of the angles the line makes at the base?

Answer 3

Excellent diagram @aum !

Answer 4

Angle BAD = Angle CAD (Given)
Angle ADB = angle ADC = 90 degrees (Given)
Therefore, angle ABD = angle ACD (because of sum of three angles of a triangle = 180 degrees).
Thus, angle ABD = angle ACD
And triangle ABC is isosceles.

Thank you @LarsEighner

Answer 5

thanks you so much:)@aum

Answer 6

You are welcome.

Answer 7

@aum thank you so much:)

Answer 8

Glad to be able to help. :)

Answer 9

From the three angles being equal and the fact that the "backbone" is identical with itself, you get that the small triangles are congruent. This shows the two sides of the original triangle are equal, but all so the line drawn in divides the base into equal parts (it is the perpendicular bisector). This is key to the ruler and compass construction of a right angle.