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Let the triangles ABC and DEF be such that ∠ABC = ∠DEF, ∠ACB = ∠DFE and ∠BAC = ∠EDF. Let L be the midpoint of BC and M be the point of EF. Consider the following statements:
Statement I: Triangle ABL and DEM are similar
Statement II: Triangle ALC is congruent to triangle DMF even if AC ≠ DF
Q. Which one of the following is correct in respect of the above statements?
  • a)
    Both Statement I and Statement II are true and Statement II is the correct explanation of Statement I
  • b)
    Both Statement I and Statement II are true and Statement II is not the correct explanation of Statement I
  • c)
    Statement I is true but Statement II is false
  • d)
    Statement I is false but Statement II is true
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Let the triangles ABC and DEF be such that ∠ABC = ∠DEF, ∠A...
Statement I:
In triangles ABC and DEF
∠ABC = ∠DEF and ∠ACB = ∠DFE [ ∵ Given]
⇒ ABC ∼ DEF [ ∵ AA ∼]
⇒ AB/DE = BC/EF
⇒ AB/DE = (BC/2)/(EF/2)
⇒ AB/DE = BL/EM [ ∵ L and M are midpoints of BC and EF respectively]
In triangle ABL and DEM
AB/DE = BL/DM [Proved]
∠ABC = ∠DEF [Given]
⇒ ABL ∼ DEM [ ∵ SAS ∼]
⇒ Statement I is true
Statement II:
For any two triangles to be congruent, their corresponding sides have to be equal
⇒ Statement II is false
∴ Only Statement I is true but statement II is false.
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Most Upvoted Answer
Let the triangles ABC and DEF be such that ∠ABC = ∠DEF, ∠A...
Statement I:
In triangles ABC and DEF
∠ABC = ∠DEF and ∠ACB = ∠DFE [ ∵ Given]
⇒ ABC ∼ DEF [ ∵ AA ∼]
⇒ AB/DE = BC/EF
⇒ AB/DE = (BC/2)/(EF/2)
⇒ AB/DE = BL/EM [ ∵ L and M are midpoints of BC and EF respectively]
In triangle ABL and DEM
AB/DE = BL/DM [Proved]
∠ABC = ∠DEF [Given]
⇒ ABL ∼ DEM [ ∵ SAS ∼]
⇒ Statement I is true
Statement II:
For any two triangles to be congruent, their corresponding sides have to be equal
⇒ Statement II is false
∴ Only Statement I is true but statement II is false.
Free Test
Community Answer
Let the triangles ABC and DEF be such that ∠ABC = ∠DEF, ∠A...
C
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Let the triangles ABC and DEF be such that ∠ABC = ∠DEF, ∠ACB = ∠DFE and ∠BAC = ∠EDF. Let L be the midpoint of BC and M be the point of EF. Consider the following statements:Statement I: Triangle ABL and DEM are similarStatement II: Triangle ALC is congruent to triangle DMF even if AC ≠ DFQ. Which one of the following is correct in respect of the above statements?a)Both Statement I and Statement II are true and Statement II is the correct explanation of Statement Ib)Both Statement I and Statement II are true and Statement II is not the correct explanation of Statement Ic)Statement I is true but Statement II is falsed)Statement I is false but Statement II is trueCorrect answer is option 'C'. Can you explain this answer?
Question Description
Let the triangles ABC and DEF be such that ∠ABC = ∠DEF, ∠ACB = ∠DFE and ∠BAC = ∠EDF. Let L be the midpoint of BC and M be the point of EF. Consider the following statements:Statement I: Triangle ABL and DEM are similarStatement II: Triangle ALC is congruent to triangle DMF even if AC ≠ DFQ. Which one of the following is correct in respect of the above statements?a)Both Statement I and Statement II are true and Statement II is the correct explanation of Statement Ib)Both Statement I and Statement II are true and Statement II is not the correct explanation of Statement Ic)Statement I is true but Statement II is falsed)Statement I is false but Statement II is trueCorrect answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Let the triangles ABC and DEF be such that ∠ABC = ∠DEF, ∠ACB = ∠DFE and ∠BAC = ∠EDF. Let L be the midpoint of BC and M be the point of EF. Consider the following statements:Statement I: Triangle ABL and DEM are similarStatement II: Triangle ALC is congruent to triangle DMF even if AC ≠ DFQ. Which one of the following is correct in respect of the above statements?a)Both Statement I and Statement II are true and Statement II is the correct explanation of Statement Ib)Both Statement I and Statement II are true and Statement II is not the correct explanation of Statement Ic)Statement I is true but Statement II is falsed)Statement I is false but Statement II is trueCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let the triangles ABC and DEF be such that ∠ABC = ∠DEF, ∠ACB = ∠DFE and ∠BAC = ∠EDF. Let L be the midpoint of BC and M be the point of EF. Consider the following statements:Statement I: Triangle ABL and DEM are similarStatement II: Triangle ALC is congruent to triangle DMF even if AC ≠ DFQ. Which one of the following is correct in respect of the above statements?a)Both Statement I and Statement II are true and Statement II is the correct explanation of Statement Ib)Both Statement I and Statement II are true and Statement II is not the correct explanation of Statement Ic)Statement I is true but Statement II is falsed)Statement I is false but Statement II is trueCorrect answer is option 'C'. Can you explain this answer?.
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