Question

e.

f.

what must be marked on the triangles below for them to be congruent by sss?

what must be marked on the triangles below for them to be congruent by asa?

Explanation:

Step1: Analyze triangle congruence for part e

For two triangles, we have two sides equal (marked) and a non - included angle. But the congruence rule \(SAS\) requires the angle to be included. So, the answer is \(No\).

Step2: Analyze triangle congruence for part f

We have two angles and a non - included side. By the \(AAS\) (Angle - Angle - Side) congruence rule, if two angles and a non - included side of one triangle are equal to the corresponding two angles and non - included side of another triangle, the triangles are congruent. So, the answer is \(Yes\) by \(AAS\).

Step3: Analyze triangle congruence for part g

We have \(QR = HG=31\), \(QS = HK = 42\), \(RS=KG = 40\). By the \(SSS\) (Side - Side - Side) congruence rule, if three sides of one triangle are equal to the three sides of another triangle, the triangles are congruent. So, the answer is \(Yes\) by \(SSS\).

Step4: Analyze for SSS congruence in the first additional question

For \(\triangle RQS\) and \(\triangle DQS\), we already have \(RQ = DQ\) (marked) and \(QS=QS\) (common side). For \(SSS\) congruence, we need \(RS = DS\).

Step5: Analyze for ASA congruence in the second additional question

For \(\triangle DEF\) and \(\triangle LKJ\), we have \(\angle D=\angle L\) (one pair of angles) and \(\angle E=\angle K\) (another pair of angles). For \(ASA\) congruence (which requires two angles and the included side), we need \(DE = LK\) (the included side between the two pairs of angles).

Answer:

e. \(No\)
f. \(Yes\) by \(AAS\)
g. \(Yes\) by \(SSS\)
For the SSS question: \(RS = DS\) must be marked.
For the ASA question: \(DE = LK\) must be marked.