name the types of triangle in which two of its altitudes lie on its produced sides
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Altitude of an isosceles triangle
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step by step explanation
an isosceles triangle (a triangle with two congruent sides), the altitude having the incongruent side as its base will have the midpoint of that side as its foot. Also the altitude having the incongruent side as its base will be the angle bisector of the vertex angle.
It is common to mark the altitude with the letter h (as in height), often subscripted with the name of the side the altitude is drawn to.
In a right triangle, the altitude drawn to the hypotenuse c divides the hypotenuse into two segments of lengths p and q. If we denote the length of the altitude by hc, we then have the relation
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