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If I is the set of isosceles triangles and E is the set of equilateral triangles, then
- a)I ⊂ E,
- b)E ⊂ I,
- c)E=I
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If I is the set of isosceles triangles and E is the set of equilateral...
Since every equilateral triangle is also an isoceles triangle then E is a subset of I.
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If I is the set of isosceles triangles and E is the set of equilateral...
Given sets:
- I: set of isosceles triangles
- E: set of equilateral triangles
To determine the relationship between these sets, we need to consider their definitions and properties.
Equilateral triangles:
- Definition: a triangle with all three sides of equal length
- Properties:
- All angles are also equal (each angle measures 60 degrees)
- Height, median, and bisector lines are concurrent
- Can be inscribed in a circle (circumcircle)
Isosceles triangles:
- Definition: a triangle with at least two sides of equal length
- Properties:
- The two equal sides have equal angles opposite them
- The third side (base) has a different angle opposite it
- Can have a height, median, and bisector line (depending on the type of isosceles triangle)
From these definitions and properties, we can see that:
- Every equilateral triangle is also an isosceles triangle (since it has at least two equal sides)
- Not every isosceles triangle is an equilateral triangle (since it doesn't necessarily have all three sides equal)
Therefore, the correct answer is option B: E is a subset of I (E ⊆ I), which means that every equilateral triangle is also an isosceles triangle.
- I: set of isosceles triangles
- E: set of equilateral triangles
To determine the relationship between these sets, we need to consider their definitions and properties.
Equilateral triangles:
- Definition: a triangle with all three sides of equal length
- Properties:
- All angles are also equal (each angle measures 60 degrees)
- Height, median, and bisector lines are concurrent
- Can be inscribed in a circle (circumcircle)
Isosceles triangles:
- Definition: a triangle with at least two sides of equal length
- Properties:
- The two equal sides have equal angles opposite them
- The third side (base) has a different angle opposite it
- Can have a height, median, and bisector line (depending on the type of isosceles triangle)
From these definitions and properties, we can see that:
- Every equilateral triangle is also an isosceles triangle (since it has at least two equal sides)
- Not every isosceles triangle is an equilateral triangle (since it doesn't necessarily have all three sides equal)
Therefore, the correct answer is option B: E is a subset of I (E ⊆ I), which means that every equilateral triangle is also an isosceles triangle.
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If I is the set of isosceles triangles and E is the set of equilateral triangles, thena)I ⊂ E,b)E ⊂ I,c)E=Id)none of theseCorrect answer is option 'B'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If I is the set of isosceles triangles and E is the set of equilateral triangles, thena)I ⊂ E,b)E ⊂ I,c)E=Id)none of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If I is the set of isosceles triangles and E is the set of equilateral triangles, thena)I ⊂ E,b)E ⊂ I,c)E=Id)none of theseCorrect answer is option 'B'. Can you explain this answer?.
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