Question

If m∠ABC = 53° and m∠ECD = 40°, which statement explains whether the AA similarity postulate can be used to determine whether ΔBAC ~ ΔEDC?

Yes, the AA similarity postulate can be used because a reflection over line f will establish that ∠ABC ≅ ∠DEC.

Yes, the AA similarity postulate can be used because a reflection over line f will establish that ≅ .

No, the AA similarity postulate cannot be used because a reflection over line f will establish that ∠ABC and ∠DEC are not congruent.

No, the AA similarity postulate cannot be used because a reflection over line f will establish that and are not congruent.

Answer 1

Similar triangles may or may not be congruent.

The true statement is (c) No, the AA similarity postulate cannot be used because a reflection over line f will establish that ∠ABC and ∠DEC are not congruent.

The given parameters are:

$\mathbf{\angle ABC = 53}$

$\mathbf{\angle ECD = 40}$

From the image of the triangles (see attachment);

The triangles are similar if:

$\mathbf{\angle ABC + \angle ECD = 90}$

Substitute the given values

$\mathbf{53 + 40 = 90}$

$\mathbf{93 = 90}$

The above equation is not true, because:

$\mathbf{93 \ne 90}$

Hence, the triangles are not similar by AA

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