# In the figure below, A, C, F, and D are collinear; B, C, and E are collinear

In the figure below, A, C, F, and D are collinear; B, C, and E are collinear; and the angles at A, E, and F are right angles, as marked. Which of the following statements is NOT justifiable from the given information?

- AB is parallel to EF
- DE is perpendicular to BE
- ∠ACB is congruent to ∠FCE
- ΔBAC is similar to ΔEFC
- CE is congruent to ED

### Answer

**The correct answer is E. **

Statement A, that AB and EF are parallel, is true because both are perpendicular to the same other line, AD.

Because ∠DEB is marked with a right angle, DE is perpendicular to BE, and so B is true.

The two angles, ∠ACB and ∠FCE, are vertical angles, so C is true.

Statement D is true because the angles in ΔBAC are congruent to the angles in ΔEFC. First, ∠A is congruent to ∠F because they are both right angles. Next, ∠ACB and ∠FCE are vertical angles. Third, the remaining angles must have the same measure because the sum of the interior angle measures in any triangle is 180°.

Statement E is not true as only if ∠ECF is congruent to ∠EDF can CE be congruent to DE.