Unizor - Geometry2D - Triangle - Mini Theorems 1
Channel: Zor Shekhtman on UNIZOR Education
Date: 2011-10-16

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1. Prove that in an isosceles triangle two medians to congruent sides are congruent.
2. Prove that in an isosceles triangle two angle bisectors to congruent sides are congruent.
3. Prove that in an isosceles triangle two altitudes to congruent sides are congruent.
4. Prove that segments of two perpendicular bisectors to two congruent sides of an isosceles triangle between midpoint of one side and crossing of its bisector with another side are congruent. 
5. Prove that a line, perpendicular to an angle bisector, cuts from two rays forming this angle congruent segments, assuming that an angle is less that 180 degrees.
6. Prove that median AM of a triangle ΔABC from vertex A to an opposite side BC is equidistant from vertices B and C.
7. Prove that the length of median AM of a triangle ΔABC from vertex A to an opposite side BC is less than half sum of lengths of sides AB and AC in lies in between.
8. Prove that sum of lengths of all three medians of a triangle is less than its perimeter, but greater than its halp-perimeter.