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The median of a triangle divides it into two
- a)congruent triangles.
- b)isosceles triangles.
- c)right angles.
- d)triangles of different areas.
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The median of a triangle divides it into twoa)congruent triangles.b)is...
Thus median of a triangle divides it into two triangles of equal area.
This question is part of UPSC exam. View all Class 9 courses
Most Upvoted Answer
The median of a triangle divides it into twoa)congruent triangles.b)is...
Explanation:
The median of a triangle is a line segment that joins a vertex of the triangle to the midpoint of the opposite side. In other words, it connects one vertex to the midpoint of the side opposite to that vertex.
When a median is drawn in a triangle, it divides the triangle into two smaller triangles.
Triangles of Different Areas:
The correct answer is option D, which states that the median divides the triangle into two triangles of different areas.
When a median is drawn in a triangle, it divides the triangle into two smaller triangles. The two smaller triangles have different areas because their bases and heights are different.
The area of a triangle is given by the formula:
Area = 0.5 * base * height
Since the two smaller triangles have different bases and heights, their areas will be different.
Let's take an example to illustrate this:
Consider a triangle ABC with side lengths AB, BC, and CA. Let's draw the median AD from vertex A to the midpoint of side BC.
Now, triangle ABC is divided into two smaller triangles: triangle ABD and triangle ACD.
Triangle ABD has base AD and height h1.
Triangle ACD has base AD and height h2.
Since h1 and h2 are different, the areas of triangle ABD and triangle ACD will be different.
Therefore, the correct answer is option D - the median of a triangle divides it into two triangles of different areas.
The median of a triangle is a line segment that joins a vertex of the triangle to the midpoint of the opposite side. In other words, it connects one vertex to the midpoint of the side opposite to that vertex.
When a median is drawn in a triangle, it divides the triangle into two smaller triangles.
Triangles of Different Areas:
The correct answer is option D, which states that the median divides the triangle into two triangles of different areas.
When a median is drawn in a triangle, it divides the triangle into two smaller triangles. The two smaller triangles have different areas because their bases and heights are different.
The area of a triangle is given by the formula:
Area = 0.5 * base * height
Since the two smaller triangles have different bases and heights, their areas will be different.
Let's take an example to illustrate this:
Consider a triangle ABC with side lengths AB, BC, and CA. Let's draw the median AD from vertex A to the midpoint of side BC.
Now, triangle ABC is divided into two smaller triangles: triangle ABD and triangle ACD.
Triangle ABD has base AD and height h1.
Triangle ACD has base AD and height h2.
Since h1 and h2 are different, the areas of triangle ABD and triangle ACD will be different.
Therefore, the correct answer is option D - the median of a triangle divides it into two triangles of different areas.
Community Answer
The median of a triangle divides it into twoa)congruent triangles.b)is...
Yes as mid point theorm do.....
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The median of a triangle divides it into twoa)congruent triangles.b)isosceles triangles.c)right angles.d)triangles of different areas.Correct answer is option 'D'. Can you explain this answer?
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