Question

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

Answer 1

Answer:

The two column proof is given as follows;

Statement              ${}$                                 Reason

1. $\overline {ABCD}$, $\overline{GD}$ \\ $\overline {AK}$, $\overline{AC}$ ≅ $\overline {DB}$      ${}$       Given

$\overline{GB}$ ⊥ $\overline {BD}$, $\overline{KC}$ ⊥ $\overline {BD}$

2. ∠KCA = ∠GBD = 90°            ${}$              Given

3. Therefore,

4. ∠KAB = ∠GDC             ${}$                       Alternate interior angles

5. ΔGBD ≅ ΔKCA            ${}$                      By ASA rule of congruency

6. $\overline{GB}$ ≅ $\overline {KC}$             ${}$                              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 $\overline{GB}$ is congruent to segment $\overline {KC}$ by Congruent Parts of Congruent Triangles are Congruent, CPCTC.