1. Prove that the angle bisectors of the angle opposite to the base of an isosceles triangle also bisects the base and is perpendicular to it

2. prove that the triangle formed by joining the midpoints of the three sides of an isosceles triangle is also isosceles

3. prove that the triangle formed by joining the midpoints of the three sides of an equilateral triangle is also equilateral

4. prove that the median to the equal sides of an isosceles triangle are equal to each other

5. prove that the median to the base of an isosceles triangle divide each other into respectively equal segments

6. prove that the median to the base of an isosceles triangle is perpendicular to the base and bisects the opposite angle

7. prove that if one of the altitudes of a triangle is also a median, then the triangle is isosceles

2. prove that the triangle formed by joining the midpoints of the three sides of an isosceles triangle is also isosceles

3. prove that the triangle formed by joining the midpoints of the three sides of an equilateral triangle is also equilateral

4. prove that the median to the equal sides of an isosceles triangle are equal to each other

5. prove that the median to the base of an isosceles triangle divide each other into respectively equal segments

6. prove that the median to the base of an isosceles triangle is perpendicular to the base and bisects the opposite angle

7. prove that if one of the altitudes of a triangle is also a median, then the triangle is isosceles

## This question was asked on Jan 14, 2013.

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