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The line segments joining the mid points of the sides of a triangle form four triangles each of which is :
- a)Similar to the original triangle
- b)Congruent to the original triangle
- c)An equilateral triangle
- d)An isosceles triangle
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The line segments joining the mid points of the sides of a triangle fo...
Given :△ABC, D, E and F are mid points of AB, BC, CA respectively.
Using mid point theorem we prove that □ADEF, □DBEF and □DECF are parallelograms. The diagonal of a parallelogram divides the parallelogram into two congruent triangles. So all triangles are congruent to each other. And each small triangle is similar to the original triangle.
Using mid point theorem we prove that □ADEF, □DBEF and □DECF are parallelograms. The diagonal of a parallelogram divides the parallelogram into two congruent triangles. So all triangles are congruent to each other. And each small triangle is similar to the original triangle.
Most Upvoted Answer
The line segments joining the mid points of the sides of a triangle fo...
Given :△ABC, D, E and F are mid points of AB, BC, CA respectively.
Using mid point theorem we prove that □ADEF, □DBEF and □DECF are parallelograms. The diagonal of a parallelogram divides the parallelogram into two congruent triangles. So all triangles are congruent to each other. And each small triangle is similar to the original triangle.
Using mid point theorem we prove that □ADEF, □DBEF and □DECF are parallelograms. The diagonal of a parallelogram divides the parallelogram into two congruent triangles. So all triangles are congruent to each other. And each small triangle is similar to the original triangle.
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The line segments joining the mid points of the sides of a triangle fo...
Explanation:
To understand why the line segments joining the midpoints of the sides of a triangle form four similar triangles, let's break down the process step by step:
Step 1: Identifying the Midpoints
The first step is to identify the midpoints of the sides of the triangle. The midpoint of a line segment is the point that divides the segment into two equal parts. For each side of the triangle, we find the midpoint.
Step 2: Joining the Midpoints
Once we have identified the midpoints, we draw line segments to join them. We draw line segments joining the midpoints of each pair of sides of the triangle. This creates four smaller triangles within the original triangle.
Step 3: Analyzing the Resulting Triangles
Now, let's analyze the resulting triangles formed by joining the midpoints:
Similarity:
The resulting triangles are similar to the original triangle. Similarity means that the corresponding angles of the triangles are equal, and the corresponding sides are proportional. In this case, we can see that the resulting triangles have the same angles as the original triangle, and the sides are in proportion.
Explanation of Similarity:
The line segments joining the midpoints divide each side of the triangle into two equal parts. This means that the resulting triangles have sides that are proportional to the sides of the original triangle. Additionally, the angles of the resulting triangles are the same as the corresponding angles of the original triangle because the line segments joining the midpoints are parallel to the sides of the triangle.
Conclusion:
In conclusion, the line segments joining the midpoints of the sides of a triangle form four triangles, each of which is similar to the original triangle. This is because the resulting triangles have the same angles as the original triangle and the sides are proportional.
To understand why the line segments joining the midpoints of the sides of a triangle form four similar triangles, let's break down the process step by step:
Step 1: Identifying the Midpoints
The first step is to identify the midpoints of the sides of the triangle. The midpoint of a line segment is the point that divides the segment into two equal parts. For each side of the triangle, we find the midpoint.
Step 2: Joining the Midpoints
Once we have identified the midpoints, we draw line segments to join them. We draw line segments joining the midpoints of each pair of sides of the triangle. This creates four smaller triangles within the original triangle.
Step 3: Analyzing the Resulting Triangles
Now, let's analyze the resulting triangles formed by joining the midpoints:
Similarity:
The resulting triangles are similar to the original triangle. Similarity means that the corresponding angles of the triangles are equal, and the corresponding sides are proportional. In this case, we can see that the resulting triangles have the same angles as the original triangle, and the sides are in proportion.
Explanation of Similarity:
The line segments joining the midpoints divide each side of the triangle into two equal parts. This means that the resulting triangles have sides that are proportional to the sides of the original triangle. Additionally, the angles of the resulting triangles are the same as the corresponding angles of the original triangle because the line segments joining the midpoints are parallel to the sides of the triangle.
Conclusion:
In conclusion, the line segments joining the midpoints of the sides of a triangle form four triangles, each of which is similar to the original triangle. This is because the resulting triangles have the same angles as the original triangle and the sides are proportional.
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The line segments joining the mid points of the sides of a triangle form four triangles each of which is :a)Similar to the original triangleb)Congruent to the original trianglec)An equilateral triangled)An isosceles triangleCorrect answer is option 'A'. Can you explain this answer?
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