CBSE Class 6 Mathematics Shapes Assignment Set 05

Question. Name the type of triangle from the following:
(i) [Triangle with three unequal sides]
(ii) [Triangle with one right angle]
(iii) [Triangle with three equal sides]
(iv) [Triangle with two equal sides]
Answer:
(i) Scalene \(\Delta\)
(ii) Right \(\Delta\)
(iii) Equilateral \(\Delta\)
(iv) Isosceles \(\Delta\)

Question. Name the type of triangle if
(a) Sides are \(7\text{ cm}\), \(8\text{ cm}\) and \(9\text{ cm}\)
(b) \(\Delta ABC\) : \(AB = AC = 6\text{ cm}\), \(BC = 8\text{ cm}\)
(c) \(\Delta ABC\) : \(AB = BC = CA = 5\text{ cm}\)
(d) \(\Delta ABC\) : \(\angle B = 90^\circ\), \(BC = 4\text{ cm}\), \(AB = 3\text{ cm}\).
Answer:
(a) Scalene
(b) Isosceles
(c) Equilateral
(d) Right angle.

Question. Name the type of triangle if
(a) \(\Delta ABC\) : \(\angle A = \angle B = \angle C = 60^\circ\)
(b) \(\Delta ABC\) : \(\angle B = \angle C = 50^\circ\)
(c) \(\Delta ABC\) : \(\angle A = 45^\circ\), \(\angle B = 45^\circ\), \(\angle C = 90^\circ\)
(d) \(\Delta ABC\) : \(\angle A = 50^\circ\), \(\angle B = 60^\circ\), \(\angle C = 70^\circ\)
Answer:
(a) Equilateral \(\Delta\)
(b) Isosceles \(\Delta\)
(c) Right angle \(\Delta\)
(d) Scalene \(\Delta\).

Question. If each side of a triangle is \(5\text{ cm}\), name the type of triangle
Answer: Equilateral \(\Delta\)

Question. Can you construct a triangle whose each angle is \(90^\circ\). If not why not?
Answer: No because sum of all angles of a \(\Delta = 180^\circ\).

Question. Take three collinear points, A, B, C (on notebook). Join AB, BC and CA. Is the figure formed a triangle. If not why?
Answer: No. Triangle cannot be formed because the points form a straight line.

Question. Take three non collinear points (A, B, C) on your note book. Join AB, BC, CA. What type of figure do you get? If it is a triangle, name the following:
(a) Side opposite to \(\angle B\)
(b) Angle opposite to side AC
(c) Vertex opposite to side BC
(d) Side opposite to vertex A, B
Answer: Scalene \(\Delta\).
(a) AC
(b) \(\angle B\)
(c) A
(d) BC, AC

Question. Distinguish between a triangle and its triangular region.
Answer: \(\Delta\) means, the figure formed by three lines and Triangular region means the area enclosed by the three lines.

Question. The measures of two angles of a triangle are \(50^\circ\) and \(60^\circ\). Find the measure of 3rd angle
Answer: \(70^\circ\)

Question. Can a triangle have:
(a) All angles equal to \(60^\circ\)
(b) All angles more than \(60^\circ\)
(c) All angles less than \(60^\circ\)
(d) Two acute angles.
(e) Two obtuse angles
(f) Two right angles.
(g) One acute and two obtuse.
Answer:
(a) yes
(b) NO
(c) NO
(d) yes
(e) NO
(f) No
(g) No