Samacheer Kalvi Class 5 Maths Solutions Term 2 Chapter 3 Patterns Exercise 3.1

Question 1. Find the angle of the given shapes using the equilateral triangle.
(i)

(ii)

Answer:
(i) The shape shown is a rhombus formed by joining two equilateral triangles. Each angle in an equilateral triangle is \(60^\circ\).

The angles at the pointed corners of the rhombus are \(60^\circ\). The angles where the two triangles meet are \(60^\circ + 60^\circ = 120^\circ\). These shapes help us understand how angles combine.
(ii) The shape shown can be interpreted as a rhombus formed by two equilateral triangles.

Similar to part (i), the acute angles are \(60^\circ\), and the obtuse angles formed by two triangles are \(120^\circ\). Understanding these basic geometric constructions helps in more complex problems.
In simple words: When two equilateral triangles are joined, the angles at the outer corners stay \(60^\circ\), but the angles where their bases meet add up to \(120^\circ\).

🎯 Exam Tip: Remember that an equilateral triangle always has three equal angles, each measuring \(60^\circ\). This is a fundamental property for solving many geometry problems.

Question 2. Find the angles of a rectangle using a circle.
Answer: We can find the angles of a rectangle by dividing the total angle of a circle. A circle has a total angle of \(360^\circ\). If we divide a circle into four equal parts, like drawing a plus sign inside it, each part forms a right angle.

Each corner of a rectangle is a right angle.
\( \text{Angle of a circle} = 360^\circ \)
\( \text{Number of equal divisions for a rectangle's corners} = 4 \)
\( \text{Each angle} = 360^\circ \div 4 = 90^\circ \)
This shows that each corner of a rectangle measures \(90^\circ\).
In simple words: A full circle is \(360^\circ\). Since a rectangle has four equal corners, we divide \(360^\circ\) by 4 to get \(90^\circ\) for each corner.

🎯 Exam Tip: Remember that the sum of angles around a point is \(360^\circ\), and all four interior angles of a rectangle are right angles, each measuring \(90^\circ\).