Here you get the CBSE Class 10 Mathematics chapter 6, Triangles: NCERT Exemplar Problems and Solutions (Part-II). This part of the chapter includes detailed solutions for all questions included in Exercise 6.2 of NCERT Exemplar Problems for Class 10 Mathematics Chapter: Triangles. This exercise comprises only the Very Short Answer Type Questions framed from various important topics in the chapter. Each question is provided with a detailed solution.
NCERT Exemplar problems are a very good resource for preparing the critical questions like Higher Order Thinking Skill (HOTS) questions. All these questions are very important to prepare for CBSE Class 10 Mathematics Board Examination 2017-2018 as well as other competitive exams.
Find below the NCERT Exemplar problems and their solutions for Class 10 Mathematics Chapter, Triangles:
Very Short Answer Type Questions
Write whether True or False and justify your answer:
Question. 1 Is the triangle with sides 25cm, 5cm and 24cm a right triangle? Give reason for your answer.
For given triangle to be a right triangle, it must satisfy Pythagoras theorem.
i.e., 252 = 52 + 242
⟹ 625 = 25 + 576
Which is not true.
So, given triangle is not a right triangle.
Question. 2 It is given that ΔDEF ~ ΔRPQ. Is it true to say that ∠ D = ∠R and ∠F = ∠P? Why?
We know that, if two triangles are similar, then their corresponding angles are equal,
Thus, in ΔDEF and ΔRPQ, we have:
∠D = ∠R, ∠E = ∠P and ∠F = ∠Q
Question. 3 A and B are respectively the points on the sides PQ and PR of a ΔPQR such that PQ = 12.5cm, PA = 5cm, BR = 6cm and PB = 4cm. Is AB || QR? Give reason for your answer.
By converse of BPT, AB will be parallel to QR if AB, divides PQ and PR in the same ratio i.e.,
Question. 4 In figure, BD and CE intersect each other at the point P. Is ΔPBC ~ ΔPDE? Why?
Question. 5 In ΔPQR and ΔMST, ∠P = 55°, ∠Q =25°, ∠M = 100° and ∠S = 25°. Is ΔQPR ~ ΔTSM? Why?
We know that, the sum of three angles of a triangle is 180°
Thus, in ΔPQP,
∠P + ∠Q + ∠R = 180°
⟹ 55° + 25° + ÐR = 180°
⟹ ∠R = 180° - (55° + 25°) = 180° - 80° =100°
Also. in ΔTSM,
∠T + ∠S + ∠M = 180°
⟹ ∠T + ∠25° + 100° = 180°
⟹ ∠T = 180o - (25° + 100°)
= 180°-125° = 55°
Question. 6 Is the following statement true? Why? "Two quadrilaterals are similar, if their corresponding angles are equal".
Two quadrilaterals will be similar, if their corresponding angles are equal and the ratio of their corresponding sides area also equal.
Question. 7 Two sides and the perimeter of one triangle are respectively three times the corresponding sides and the perimeter of the other triangle. Are the two triangles similar? Why?
Here, the corresponding two sides and the perimeters of two triangles are proportional, then third side of both triangles will also be in proportion.
Question. 8 If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle. Can you say that two triangles will be similar? Why?
Thus, ΔABC ~ ΔPQR [By AAA similarity criterion]
So, given statement is not correct.
Question. 10 D is a point on side QR of ΔPQR such that PD ⏊ QR. Will it be correct to say that ΔPQD ~ ΔRPD? Why?
Here, no other sides or angles are equal, so ΔPQD is not similar to ΔRPD.
Question. 11 In figure, if ∠D = ∠C, then it is true that ΔADE ~ ΔACB? Why?
Question. 12 Is it true to say that, if in two triangles, an angle of one triangle is equal to an angle of another triangle and two sides of one triangle are proportional to the two sides of the other triangle, then the triangles are similar? Give reason for your answer.
Considering the SAS similarity criterion, if one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar. But here, one angle and two sides of two triangles are equal but these sides not including equal angle, so given statement is not correct.