Question

Decide whether the two triangles must be congruent. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

Short answer

No congruence can be deduced

Step-by-step solution

Step 1. First observation from figure.

Line segments $\overline{AC}$and $\overline{BD}$are congruent

So,$\overline{AC}\cong \overline{BD}$

Step 2. Second observation from figure.

Line segments $\overline{CF}$and $\overline{DF}$are congruent

So,$\overline{CF}\cong \overline{DF}$

Step 3. Third observation from figure.

$\angle AFC$and$\angle DFB$ are vertically opposite angles and thus congruent

So,$\angle AFC\cong \angle DFB$

Step 4. Conclude given two triangles are congruent or not.

From step 1, 2, and 3

Two sides and one angle is congruent

But it does not satisfies any postulate

Thus, congruency cannot be deduced