Question

1. whats wrong with this picture of △trg? explain.

Explanation:

Step1: Use the property of similar triangles

Since \( \triangle T LN\) and \( \triangle TRG\) are similar (by AA similarity, as \( \angle T\) is common and \( \angle TLN=\angle TRG = 72^{\circ}\), \( \angle T NL=\angle TGR=72^{\circ}\) if we consider the parallel - like situation assumed from the figure's structure). For similar triangles, the ratio of corresponding sides is equal. Also, in \( \triangle TRG\), if \(TL = TN\) (marked with equal segments on \(T R\) and \(T G\)), then \(LR = NG\).

Step2: Use the angle - side relationship

In a triangle, equal sides are opposite equal angles. In \( \triangle T LN\), if \(TL = TN\), then \( \angle TLN=\angle TNL\). In \( \triangle TRG\), if \(TR = TG\) (because \(TL + LR=TN + NG\) and \(TL = TN\), \(LR = NG\)), then \( \angle TRG=\angle TGR\). But \(72^{\circ}
eq74^{\circ}\).

Answer:

The angles \( \angle TLN = 72^{\circ}\) and \( \angle TRG = 74^{\circ}\) (also \( \angle TNL = 72^{\circ}\) and \( \angle TGR = 74^{\circ}\)) contradict the angle - side relationship in triangles. If \(TL = TN\) (on \(TR\) and \(TG\) with equal segment markings) and \(LR = NG\) (so \(TR = TG\)), then \( \angle TRG\) and \( \angle TGR\) should be equal, but \(72^{\circ}
eq74^{\circ}\).