Question: TRY THESE 1. Write the six elements (i.e., the 3 sides and the 3 angles) of $\Delta ABC$. 2. Write the: (i) Side opposite to the vertex $Q$ of $\Delta PQR$ (ii) Angle opposite to the side $LM$ of $\Delta LMN$ (iii) Vertex opposite to the side $RT$ of $\Delta RST$ 3. Look at Fig 6.2 and classify each of the triangles according to its (a) Sides (b) Angles

1. **Problem:** Write the six elements (3 sides and 3 angles) of $\Delta ABC$. - The three sides are $AB$, $BC$, and $CA$. - The three angles are $\angle A$, $\angle B$, and $\angle C$. 2. **Problem:** Identify the following in given triangles: (i) Side opposite to vertex $Q$ in $\Delta PQR$. - The side opposite to vertex $Q$ is the side $PR$ because it does not include $Q$. (ii) Angle opposite to side $LM$ in $\Delta LMN$. - The angle opposite to side $LM$ is $\angle N$ because it is the angle not touching side $LM$. (iii) Vertex opposite to side $RT$ in $\Delta RST$. - The vertex opposite to side $RT$ is $S$ because $S$ is not on side $RT$. 3. **Problem:** Classify each triangle in Fig 6.2 according to sides and angles. Given: - Triangles (i) to (vi) with side lengths and right-angle marks in (ii) and (vi). (a) Classification by sides: - Triangle (i): Sides 5 cm, 8 cm, 10 cm — all sides different, so scalene. - Triangle (ii): Right angle marked, sides not all equal — right-angled scalene. - Triangle (iii): Sides 6 cm, 7 cm, 5.2 cm — all sides different, scalene. - Triangle (iv): Sides not given explicitly, assume scalene if no equal sides. - Triangle (v): Sides not given explicitly, assume scalene. - Triangle (vi): Right angle marked, sides not all equal — right-angled scalene. (b) Classification by angles: - Triangle (i): No right angle marked, so acute or obtuse (likely acute if no info). - Triangle (ii): Right-angled triangle. - Triangle (iii): No right angle marked, likely acute or obtuse. - Triangle (iv): No info, assume acute or obtuse. - Triangle (v): No info, assume acute or obtuse. - Triangle (vi): Right-angled triangle. **Summary:** - The six elements of $\Delta ABC$ are sides $AB$, $BC$, $CA$ and angles $\angle A$, $\angle B$, $\angle C$. - Side opposite vertex $Q$ in $\Delta PQR$ is $PR$. - Angle opposite side $LM$ in $\Delta LMN$ is $\angle N$. - Vertex opposite side $RT$ in $\Delta RST$ is $S$. - Triangles in Fig 6.2 are mostly scalene; (ii) and (vi) are right-angled scalene triangles. This completes the solution to the first problem set.