ABCD, GB is parallel to AK, AC is congruent to DB, GB is perpendicular to BD, KC is perpendicular to AC Prove: GB is congruent to KC

USE STATEMENT AND REASONS

The two column proof is given as follows;

Statement                                               Reason

1. , \\ , ≅             Given

⊥ , ⊥

2. ∠KCA = ∠GBD = 90°                          Given

3. Therefore,

4. ∠KAB = ∠GDC                                   Alternate interior angles

5. ΔGBD ≅ ΔKCA                                  By ASA rule of congruency

6. ≅                                          By CPCTC

Explanation:

Given that two angles and an included side of triangle ΔGBD are equal to the corresponding two angles and an included side of triangle ΔKCA, therefore, ΔGBD ≅ ΔKCA by the Ange-Side-Angle rule of congruency, therefore, we have;

Segment is congruent to segment by Congruent Parts of Congruent Triangles are Congruent, CPCTC.