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?

1. AB is parallel to EF
2. DE is perpendicular to BE
3. ∠ACB is congruent to ∠FCE
4. ΔBAC is similar to ΔEFC
5. 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.