Can you think of a triangle in which two altitudes of the triangle are two of its sides

Answer

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Hint: Learn the properties of type of triangle and try to differentiate between them. Start solving this question by mentioning the respective properties which are related to altitudes and sides because the questions clearly mention that we have to find the name of the triangle in which two altitudes of the triangle are two of its sides.

Complete step-by-step answer:

Start with explain the properties of each optionOption A – An isosceles triangle is a triangle that has two equal sides and the angles opposite the equal sides are also equal and they are called the base angles. In an isosceles triangles ( a triangle with two congruent sides), the altitude having the incongruent side as its base will have midpoint of that side as its foot and according to the congruence tests if the triangle, two altitudes are of equal length , then the triangle is isosceles.Option B – In the right angle triangle one of its sides equal to ${90^ \circ }$. The side opposite the ${90^ \circ }$ angle is called the hypotenuse , and is the longest side of the triangle. In the right angle triangle altitude bisect the triangle in two equal triangles.Option C – An equilateral triangle three of its sides are equal and all the three angles are also equal and each measures ${60^ \circ }$. The altitude in the equilateral triangle is the line segment from the vertex that is perpendicular to the opposite side. Option D – A scalene triangle is a triangle that has no equal sides. In scalene triangle angles are also not equal . The altitude in the scalene triangle is the line segment from the vertex that is perpendicular to the line containing the base. After considering all the options we find that option A is correct.

So, the correct answer is “Option A”.

Note: Students might get confused between isosceles triangle and equilateral triangle because they both have equal sides.We also differentiate between the right angle triangle and isosceles triangle because the altitude bisect the triangle in two equal parts