Question

geometry with statistics honors - ferraro - 2 - a
topic 4: readiness assessment
is △fba the same size and shape as △fce? explain.
a. yes; △fba is a reflection of △fce.
b. no; the triangles have the same angle measures, but there is no information about the sides.
c. yes; △fba is a rotation of △fce.
d. no; the triangles have different angle measures and side lengths.

Explanation:

Step1: Recall congruence criteria

For two triangles to be the same size and shape (congruent), we need information about side - lengths and angle - measures. We have vertical angles at point F, so ∠BFA = ∠CFE. But we have no information about side - lengths such as whether BF = CF, AF = EF or AB = CE.

Step2: Analyze options

Option A: There is no indication of a reflection. Option B: Since we only know about vertical angles (equal angle measures) and no side - length information, the triangles may be similar (same shape, equal angle measures) but not necessarily congruent (same size and shape). Option C: There is no indication of a rotation. Option D: We don't know for sure that they have different angle measures and side - lengths as we only lack side - length information and have equal vertical angles.

Answer:

B. No; the triangles have the same angle measures, but there is no information about the sides.