The given altitude of triangle ABC is h, is located inside the triangle and
extends from side AB to the vertex C.
The true statements are;
I. Triangle ABC could be a right triangle
II. Angle C cannot be a right angle
Reasons:
I. Triangle ABC could be a right triangle
The altitude drawn from the vertex C to the line AB = h
The length of h = AB
Where, triangle ABC is a right triangle, we have;
The legs of the right triangle are; h and AB
The triangle ABC formed is an isosceles right triangle
Therefore, triangle ABC could be an isosceles right triangle; True
II. Angle C cannot be a right angle: True
If angle ∠C is a right angle, we have;
AB = The hypotenuse (longest side) of ΔABC
Line h = AB is an altitude, therefore, one of the sides of ΔABC is hypotenuse to h, and therefore, longer than h and AB, which is false
Therefore, ∠C cannot be a right angle
III. Angle C could be less than 45 degrees; False
The minimum value of angle C is given by when triangle ABC is an isosceles right triangle. As the position of h shifts between AB, the lengths of one of the sides of ΔABC increases, and therefore, ∠C, increases
Therefore, ∠C cannot be less than 45°
The true statements are I and II
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