Question

prove the following statement using the given pieces of information. given: ∠gks ≅ ∠jks, ks⊥gj. prove: △sgk ≅ △sjk. complete the two - column proof by filling in the blanks. statements reasons 1 ks⊥gj 1 given 2 ∠ksg and ∠ksj are right angles 2 dropdown with options: alternate interior angles converse theorem, vertical angles theorem, right angles congruent theorem, definition of ⊥

Explanation:

Step1: Recall perpendicular - definition

If a line is perpendicular to another line, the angles formed are right - angles. Given $KS\perp GJ$, by the definition of $\perp$, $\angle KSG$ and $\angle KSJ$ are right angles.

Step2: Identify congruent parts

We are given that $\angle GKS\cong\angle JKS$ and $KS = KS$ (reflexive property). Since $\angle KSG\cong\angle KSJ$ (right angles are congruent) and we have a pair of congruent angles and the included side between them, by the Angle - Side - Angle (ASA) congruence criterion, $\triangle SGK\cong\triangle SJK$.
The reason for the statement “$\angle KSG$ and $\angle KSJ$ are right angles” is the Definition of $\perp$.

Answer:

Definition of $\perp$