Answer:
The two column proof is given as follows;
Statement [tex]{}[/tex] Reason
1. [tex]\overline {ABCD}[/tex], [tex]\overline{GD}[/tex] \\ [tex]\overline {AK}[/tex], [tex]\overline{AC}[/tex] ≅ [tex]\overline {DB}[/tex] [tex]{}[/tex] Given
[tex]\overline{GB}[/tex] ⊥ [tex]\overline {BD}[/tex], [tex]\overline{KC}[/tex] ⊥ [tex]\overline {BD}[/tex]
2. ∠KCA = ∠GBD = 90° [tex]{}[/tex] Given
3. Therefore,
4. ∠KAB = ∠GDC [tex]{}[/tex] Alternate interior angles
5. ΔGBD ≅ ΔKCA [tex]{}[/tex] By ASA rule of congruency
6. [tex]\overline{GB}[/tex] ≅ [tex]\overline {KC}[/tex] [tex]{}[/tex] 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 [tex]\overline{GB}[/tex] is congruent to segment [tex]\overline {KC}[/tex] by Congruent Parts of Congruent Triangles are Congruent, CPCTC.
