DAV Class 7 Maths Chapter 10 Worksheet 3
Construction of Triangles Worksheet 3
1. Construct a triangle ABC in which BC = 4 cm \( \angle B = 50^\circ \) and \( \angle C = 70^\circ \).
Answer
2. Draw a triangle ABC in which BC = 8 cm, \( \angle B = 50^\circ \), and \( \angle A = 50^\circ \). Also bisect \( \angle A \text{ and } \angle C \).
Answer
\[ \begin{align*} In \ \triangle ABC \\ \angle A + \angle B + \angle C & = 180^\circ \\ 50^\circ + 50^\circ + \angle C & = 180^\circ \\ 100^\circ + \angle C & = 180^\circ \\ \angle C & = 180^\circ - 100^\circ \\ \angle C & = 80^\circ \end{align*} \]
3. Draw a triangle ABC with AB = 4.5 cm, \( \angle ABC = 35^\circ \), and \( \angle ACB = 65^\circ \).
Answer
\[ \begin{align*} In \ \triangle ABC \\ \angle A + \angle B + \angle C & = 180^\circ \\ \angle A + 35^\circ + 65^\circ & = 180^\circ \\ \angle A + 100^\circ & = 180^\circ \\ \angle A & = 180^\circ - 100^\circ \\ \angle A & = 80^\circ \end{align*} \]
4. Construct a triangle PQR with \( PQ = 7.5 cm, \angle RPQ = 45^\circ , \angle RQP = 45^\circ \). Measure the third angle. What kind of a triangle is it?
Answer
\( \angle R = 90^\circ . \ \triangle PQR \) is a right angled triangle.
5. Construct a triangle PQR with \( \angle P = 70^\circ , \angle Q = 120^\circ \text{ and side } PQ = 5.2 cm \). Is the construction possible ?
Answer
No, construction is not possible.
6. Construct a triangle ABC in which BC = 6 cm \( \angle B = 40^\circ \) and \( \angle C = 110^\circ \).
Answer