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Question: Which of the following statements is true if m∠E = m∠Y and m∠F = m∠X?

triangle-images2

Options:

  1.  m∠E  >  m∠Z
  2.  The measure of each segment in ΔYXZ is three times the size of those in ΔEFG.
  3.  ΔEFG ≅ ΔYXZ
  4.  There is a sequence of rigid motions and dilations that map ΔEFG onto ΔYXZ.

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1 Answer

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Best answer

3. ΔEFG ≅ ΔYXZ

ΔEFG ≅ ΔYXZ is true if m∠E = m∠Y and m∠F = m∠X.


Solution:

Given conditions:

  • m∠E = m∠Y and
  • m∠F = m∠X

The above angles are corresponding angles, and they are also congruent angles.

This implies that:
The triangles are similar (not congruent) by AA postulate.

So, we have: ΔEFG ≅ ΔYXZ

Hence, the true statement is 3. ΔEFG ≅ ΔYXZ

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