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Which of the following statements is CORRECT?
  • a)
    The ratio of the areas of two similar triangles is equal to the ratio of their corresponding sides.
  • b)
    If a line is drawn parallel to one side of the triangle to intersect the other two sides in distinct points then the other two sides are divided in the same ratio.
  • c)
    All similar figures are congruent.
  • d)
    If in two triangles, two angles of one triangle is equal to the two angles of the other triangle then two triangles may or may not be congruent.
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Which of the following statements is CORRECT?a)The ratio of the areas ...
Explanation:

Statement a: The ratio of the areas of two similar triangles is equal to the ratio of their corresponding sides.
- This statement is incorrect. The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Statement b: If a line is drawn parallel to one side of the triangle to intersect the other two sides in distinct points then the other two sides are divided in the same ratio.
- This statement is correct. This property is known as the Basic Proportionality Theorem (BPT) and is used to find unknown sides of similar triangles.

Statement c: All similar figures are congruent.
- This statement is incorrect. Similar figures have the same shape but not necessarily the same size, whereas congruent figures have the same shape and size.

Statement d: If in two triangles, two angles of one triangle is equal to the two angles of the other triangle then two triangles may or may not be congruent.
- This statement is correct. Two triangles with the same angle measures are not necessarily congruent, as the side lengths may differ.

Therefore, option B is the correct statement.
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Community Answer
Which of the following statements is CORRECT?a)The ratio of the areas ...
BPT (Basic proportional theorem) states that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points then the other two sides are divided in the present ratio.
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Which of the following statements is CORRECT?a)The ratio of the areas of two similar triangles is equal to the ratio of their corresponding sides.b)If a line is drawn parallel to one side of the triangle to intersect the other two sides in distinct points then the other two sides are divided in the same ratio.c)All similar figures are congruent.d)If in two triangles, two angles of one triangle is equal to the two angles of the other triangle then two triangles may or may not be congruent.Correct answer is option 'B'. Can you explain this answer?
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