GSEB Class 6 Maths Solutions Chapter 5 Understanding Elementary Shapes Exercise 5.6

Question 1. Name the type of following triangles:
(a) Triangle with lengths of sides 7 cm, 8 cm and 9 cm.
(b) \( \triangle ABC \) with AB = 8.7 cm, AC = 7 cm and BC = 6 cm.
(c) \( \triangle PQR \) such that PQ = QR = PR = 5 cm.
(d) \( \triangle DEF \) with \( m\angle D = 90^\circ \)
(e) \( \triangle XYZ \) with \( m\angle Y = 90^\circ \) and XY = YZ.
(f) \( \triangle LMN \) with \( m\angle L = 30^\circ \), \( m\angle M = 70^\circ \) and \( m\angle N = 80^\circ \)
Answer:
(a) Since the side lengths are 7 cm, 8 cm, and 9 cm, all sides have different measures. Therefore, this triangle is a scalene triangle.
(b) Since the side lengths AB = 8.7 cm, AC = 7 cm, and BC = 6 cm, all sides have different measures. So, \( \triangle ABC \) is a scalene triangle.
(c) Since PQ = QR = PR = 5 cm, all three sides of \( \triangle PQR \) are equal. This means \( \triangle PQR \) is an equilateral triangle.
(d) Since one angle, \( m\angle D \), is \( 90^\circ \), \( \triangle DEF \) is a right-angled triangle.
(e) Since \( m\angle Y = 90^\circ \) and two sides, XY and YZ, are equal, \( \triangle XYZ \) is an isosceles right triangle.
(f) Since all angles, \( m\angle L = 30^\circ \), \( m\angle M = 70^\circ \), and \( m\angle N = 80^\circ \), are less than \( 90^\circ \), all angles of \( \triangle LMN \) are acute. Thus, \( \triangle LMN \) is an acute-angled triangle.
In simple words: Look at the sides and angles of each triangle. If all sides are different, it's scalene. If all sides are equal, it's equilateral. If two sides are equal, it's isosceles. If it has a \( 90^\circ \) angle, it's right-angled. If all angles are less than \( 90^\circ \), it's acute. If one angle is more than \( 90^\circ \), it's obtuse.

Exam Tip: Remember to classify triangles by both their sides (scalene, isosceles, equilateral) and their angles (acute, right, obtuse) to give a complete description if possible.

Question 2. Mach the following:
Answer: The correct matches for the triangle measures and types are shown in the table below.

Exam Tip: Understand the definitions of each triangle type. This knowledge helps to quickly match their characteristics with their names.

Question 3. Name each of the following triangles in two different ways: (you may judge the nature of the angle by observation)
Answer:
(a) (i) Acute-angled triangle (ii) Isosceles triangle
(b) (i) Right-angled triangle (ii) Right triangle
(c) (i) Obtuse-angled triangle (ii) Isosceles triangle
(d) (i) Right-angled triangle (ii) Isosceles triangle
(e) (i) Acute-angled triangle (ii) Equilateral triangle
(f) (i) Obtuse-angled triangle (ii) Scalene triangle
In simple words: We give two names for each triangle shown. One name tells about its angles (like acute, right, or obtuse), and the other name tells about its sides (like isosceles, equilateral, or scalene).

Exam Tip: Always categorize a triangle using both its side properties and its angle properties for a complete description.

Question 4. Try to construct triangles using matchsticks. Some are shown here. Can you make a triangle with
(a) 3 matchsticks?
(b) 4 matchsticks?
(c) 5 matchsticks?
(d) 6 matchsticks?
(Remember you have to use all the available matchsticks in each case)
Name the type of triangle in each case. If you cannot make a triangle, think of reasons for it.
Answer:
(a) Yes, we can construct an equilateral triangle using 3 matchsticks, as shown in the diagram.
(b) No, we cannot form a triangle with 4 matchsticks. The rule says that the sum of any two sides must be greater than the third side, and this condition cannot be met here. For example, if you try to make sides 1, 1, and 2, then \( 1 + 1 \) is not greater than 2.
(c) Yes, an isosceles triangle can be constructed using 5 matchsticks, as shown in the diagram. For instance, if the sides are 2, 2, and 1 matchsticks, it forms an isosceles triangle.
(d) Yes, an equilateral triangle can be formed using 6 matchsticks, as shown in the diagram. For example, by creating sides of 2, 2, and 2 matchsticks.
In simple words: We try to build triangles with different numbers of matchsticks. We make sure all matchsticks are used, and that the rule "two sides must be longer than the third side" is followed.

Exam Tip: Remember the triangle inequality theorem: the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This is crucial for constructing triangles.