Here you get the CBSE Class 10 Mathematics chapter 6, Triangles: NCERT Exemplar Problems and Solutions (Part-IA). This part of the chapter includes solutions of Question Number 1 to 6 from Exercise 6.1 of NCERT Exemplar Problems for Class 10 Mathematics Chapter: Triangles. This exercise comprises only the Multiple Choice Questions (MCQs) 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:
Multiple Choice Questions (Q. No. 1-6)
Question. 1 In figure, if ∠BAC = 90o and AD ^ BC. Then,
Consider the following diagram:
Question. 2 If the Lengths of the diagonals of rhombus are 16 cm and 12 cm. Then, the Length of the sides of the rhombus is
Given, AC = 16cm and BD = 12cm
As the diagonals of a rhombus are perpendicular bisectors of each other.
⟹ AO = 8cm, BO = 6cm and ÐAOB = 90° ….(i)
Using Pythagoras theorem in right angled ΔAOB, w have
AB2 = AO2 + OB2
⟹ AB2 = 82 + 62 [Using (i)]
⟹ AB = 10cm.
Thus length of each side of rhombus is 10 cm.
Question. 3 If DABC ~ DEDF and DABC is not similar to DDEF, then which of the following is not true?
(a) BC.EF = AC.FD
(b) AB.EF = AC.DE
(c) BC.DE = AB.EF
(d)BC.DE = AB.FD
Hence, option (b) is also true.
This expression shows that sides of one triangle DCAB are proportional to the sides of the other triangle DPQR and their corresponding angles are also equal.
Therefore, DPQR ~ DCAB.
Question. 5 In figure, two line segments AC and BD intersect each other at the point P such that PA = 6cm, PB = 3cm, PC = 2.5cm, PD = 5cm, ÐAPB = 50° and ÐCDP = 30°. Then, ÐPBA is equal to
Thus, ÐPBA = 100° verifies the option (d).
Question. 6 If in two triangles DEF and PQR, ÐD = ÐQ and ÐR = ÐE, then which of the following is not true?