CBSE Class 9 Mathematics Triangles Worksheet Set 02

OBJECTIVE: To verify that if two sides of a triangle are unequal, the longer side has a greater angle opposite to it (by paper cutting and pasting method).

DESIGN AND OR APPROACH TO THE ACTIVITY: 1) Knowledge of the fact that only angles opposite to equal sides of a triangle are equal. 2) Comparison of angles magnitude by paper cutting and pasting method.

PROCEDURE: 1) Draw any triangle \(ABC\) with unequal sides, say, \(AB = 6\text{ cm}\), \(BC = 7\text{ cm}\) and \(AC = 8\text{ cm}\) as shown in fig(i). 2) With the help of a protractor, measure the three angles of \(\triangle ABC\). 3) Make cut-outs of \(\angle A\), \(\angle B\) and \(\angle C\) in triplicate and colour them with different colours.

Question 1. Perform the measurement of the three angles of triangle ABC and verify the relationship between the sides and their opposite angles.
Answer: On measuring, we find that \(\angle B = 75^{\circ}\), \(\angle C = 47^{\circ}\) and \(\angle A = 58^{\circ}\).
On comparing the measurements of the three angles, we find that \(\angle B > \angle A\), \(\angle B > \angle C\) and \(\angle A > \angle C\).
(i) \(AC > BC\) and \(\angle B > \angle A\)
(ii) \(AC > AB\) and \(\angle B > \angle C\)
(iii) \(BC > AB\) and \(\angle A > \angle C\)
Thus, we observe that the longer side has a greater angle opposite to it.
Since \(AC > BC > AB\), we find that \(\angle B > \angle A > \angle C\).
The same is observed by comparing the cut-outs of \(\angle A\), \(\angle B\) and \(\angle C\). Hence verified.
In simple words: The longest side of a triangle always faces the largest angle, and the shortest side faces the smallest angle.

Exam Tip: Remember the theorem statement clearly: "If two sides of a triangle are unequal, the longer side has greater angle opposite to it." This is frequently used in geometric proofs.

Students must free download and practice these worksheets to gain more marks in exams. CBSE Class 9 Mathematics Worksheet - Triangles