Question

quadrilateral strk is shown, where st ≅ rk and ks ≅ tr. which of the statements is true? △skt ≅ △rtk by sas congruence. △kts ≅ △tkr by ssa congruence. △kst ≅ △trk by sss congruence. △stk ≅ △rkt by asa congruence.

Explanation:

Step1: Recall congruence criteria

• SSS (Side - Side - Side): If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
• SAS (Side - Angle - Side): If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
• ASA (Angle - Side - Angle): If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.
• SSA (Side - Side - Angle): Not a valid congruence criterion in general.

Step2: Analyze the triangles

Given \(ST\cong RK\) and \(KS\cong TR\), and \(KT\) is a common side.
For \(\triangle KST\) and \(\triangle TRK\):

• \(KS = TR\) (given)
• \(ST=RK\) (given)
• \(KT = TK\) (common side)

So, by SSS congruence criterion \(\triangle KST\cong\triangle TRK\)

Answer:

\(\triangle KST\cong\triangle TRK\) by SSS congruence.