Question

6 multiple choice 1 point state what additional information is needed to prove the triangles are congruent using sas: hj ≅ rt hi ≅ st ij ≅ st not possible

Explanation:

Step1: Recall the SAS (Side - Angle - Side) congruence criterion

The SAS congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Step2: Identify the given information

From the figure, we can assume that \(\angle I\cong\angle S\) (the angles) and \(HI\cong ST\) (the marked sides).

Step3: Determine the additional side needed

For \(\triangle HIJ\) and \(\triangle STR\), if we want to use SAS, we need the side adjacent to the given angle in each triangle. So we need \(IJ\cong RT\). But looking at the options:

• Option \(HJ\cong RT\): \(HJ\) is not adjacent to \(\angle I\) in \(\triangle HIJ\)
• Option \(HI\cong ST\): This is already a given (marked)
• Option \(IJ\cong ST\): \(IJ\) should be congruent to \(RT\) not \(ST\)

Answer:

not possible