EN हिं

NCERT Solutions Ganita Prakash (Part 1) Chapter 7 .3 Construction of Triangles When Some Sides and Angles are Given — In-text Questions

Book page 1607 Updated on2026-09-05

Q1.
How do we construct a triangle if two sides and the angle included between them are given?
Answer

Draw one given side as the base, build the given angle at one end, and cut off the second side along the new arm.

  1. Draw the first given side as the base.
  2. At the end where the angle sits, use a protractor to draw the second arm of the angle.
  3. Along that arm, mark off the second given length.
  4. Join the marked point to the far end of the base.
Tip: The included angle is the angle between the two given sides — both sides are arms of that angle. Measurements are usually written in the order side, angle, side, as in 4 cm, 60°, 3 cm.
Q2.
Construct a triangle ABC with AB = 5 cm, AC = 4 cm and ∠A = 45°.
Answer

Take AB as the base, since the given angle sits at A.

  1. Step 1: Construct a side AB of length 5 cm.
  2. Step 2: Construct ∠A = 45° by drawing the other arm of the angle.
  3. Step 3: Mark the point C on the other arm such that AC = 4 cm.
  4. Step 4: Join BC to get the required triangle.
A B C 45° 5 cm 4 cm
Base AB = 5 cm, ∠A = 45° drawn with a protractor, AC = 4 cm cut off along the new arm.
Why it happens: Once the angle at A is fixed, the whole arm AC is fixed as a direction. Marking 4 cm along it fixes C exactly. There is no choice left, so this construction gives exactly one triangle.
Was this helpful? Report an error