RBSE Solutions Class 9 Maths Chapter 8 Construction of Triangles Exercise 8.2

Chapter 8 Construction Of Triangles Ex 8.2

Case II: To Construct A Triangle Whose Two Sides And Included Angle Is Given.

Question 1. Construct a triangle ABC where a = 4 cm, b = 5 cm and \( \angle \text{C} = 60^\circ \).
Answer: First, draw a line segment CA of length 5 cm as the base. At point C, use a compass to construct an angle of 60 degrees. Then, with C as the center, draw an arc with a radius of 4 cm which intersects the arm of the 60-degree angle. Label this intersection point as B. Finally, connect point B to point A to complete the triangle ABC. This method uses two sides and the angle between them to form a unique triangle.
In simple words: To make this triangle, first draw the base measuring 5 cm. Then, at one end of the base, draw a 60-degree angle. From that same end, measure 4 cm along the angle line and mark a point. Finally, connect that point to the other end of the base to complete the triangle.

🎯 Exam Tip: When constructing triangles, always start by drawing the base. Carefully measure angles and lengths to ensure accuracy. Practice drawing the rough sketch first to plan your construction.

Question 2. Construct a triangle LMN where \( \angle \text{L} =120^\circ \), LM = 4 cm and LN = 5 cm.
Answer: Begin by drawing a line segment LM, which will be the base, measuring 4 cm. At point L, construct an angle of 120 degrees using a compass. Next, with L as the center, draw an arc with a radius of 5 cm along the arm of the 120-degree angle. Label the point where this arc intersects the angle arm as N. Finally, connect point M to point N to complete triangle LMN. This process uses two sides and their included angle.
In simple words: Start by drawing a 4 cm line for LM. At point L, draw a 120-degree angle. Measure 5 cm along the angle line from L and mark N. Then connect M to N to finish the triangle.

🎯 Exam Tip: When dealing with obtuse angles like 120 degrees, make sure to extend the line beyond 90 degrees accurately. Always clearly label all vertices and side lengths in your construction.

Question 3. Construct a \( \Delta \text{ABC} \) where AB = AC = 8 cm, \( \angle \text{A} = 15^\circ \). Draw a bisector of \( \angle \text{B} \) which meets the opposite side.
Answer: First, draw a line segment AB of length 8 cm as the base. At point A, construct an angle of 75 degrees. Using A as the center, draw an arc with a radius of 8 cm which intersects the arm of the 75-degree angle; label this point as C. Connect point C to point B to complete triangle ABC. Then, construct the angle bisector for angle B. This bisector line should extend until it meets the opposite side AC at a point, which we will label E. This creates the isosceles triangle ABC with the bisector of angle B.
In simple words: First, draw a 8 cm base AB. At point A, draw a 75-degree angle. From A, measure 8 cm along the angle line to find point C. Join C to B. Then, draw a line from B that splits angle B exactly in half, making sure it touches the side AC at point E.

🎯 Exam Tip: For constructions involving angle bisectors, ensure your compass arcs are clear and intersect precisely. Remember that in an isosceles triangle, the angles opposite the equal sides are also equal, which can help verify your construction.

Question 4. Construct an isosceles triangle ABC where one of the equal sides (BC) is 5.5 cm, and the vertex angle at B is 120 degrees.
Answer: Start by drawing a line segment BC, which will be one of the equal sides, measuring 5.5 cm. At point B, construct a vertex angle of 120 degrees. With B as the center, draw an arc with a radius of 5.5 cm along the arm of the 120-degree angle; label this point as A. Finally, connect point A to point C to complete the isosceles triangle ABC. This method creates an isosceles triangle where the vertex angle at B is 120 degrees and the sides AB and BC are equal.
In simple words: Draw a 5.5 cm line from B to C. At B, make a 120-degree angle. From B, measure 5.5 cm along the angle line and mark A. Then connect A and C. This forms a triangle with two equal sides and a 120-degree angle at B.

🎯 Exam Tip: When constructing isosceles triangles with a given vertex angle, remember that the two sides forming that angle are equal. Always double-check your angle measurement, especially for obtuse angles.