DAV Class 7 Maths Chapter 10 Worksheet 1
Construction of Triangles Worksheet 1
1. Construct a triangle LMN in which LM = 5 cm, MN = 5.6 cm and NL = 4.2 cm.
Answer
2. Draw a triangle DEF such that DE = DF = 4 cm and EF = 6 cm. Measure \( \angle E \) and \( \angle F \) .
Answer
\( \angle E = {\color{red} 40^\circ} , \angle F = {\color{red} 40^\circ} \)
3. Draw an equilateral triangle one of whose sides is of length 5 cm.
Answer
\( \angle E = {\color{red} 40^\circ} , \angle F = {\color{red} 40^\circ} \)
4. Draw a triangle PQR in which PQ = 3 cm, QR = 4 cm, and RP = 5 cm. Also, draw the perpendicular to side PQ.
Answer
XY is perpendicular to side PQ.
5. Is it possible to construct a triangle whose sides are 3 cm, 6.1 cm, and 2.6 cm?
Answer
The sum of the lengths of any two sides of a triangle is greater than the length of third side.
\begin{align*} \text{Sum of two sides} && \quad \text{Third Side} \\ \end{align*} \begin{align*} 3 + 6.1 &= 9.1 & > && 2.6 \\ 2.6 + 6.1 &= 8.7 & > && 3 \\ 3 + 2.6 &= 5.6 & \color{red}{<} && 6.1 \\ \end{align*}
Triangle is not possible.
6. Draw a triangle PQR in which PQ = 7 cm, QR = 3 cm, RP = 4 cm. Is the construction of possible?
Answer
No, the construction is not possible.
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
\begin{align*} \text{Sum of two sides} && \quad \text{Third Side} \\ \end{align*} \begin{align*} 7 + 3 &= 10 & > && 4 \\ 7 + 4 &= 11 & > && 3 \\ 3 + 4 &= 7 & \color{red}{=} && 7 \\ \end{align*}