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

Question

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

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.

Answer 1

3. ΔEFG ≅ ΔYXZ

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

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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