In this article we will share latest MP Board Class 10th Mathematics Solutions Chapter 6 Triangles Ex 6.1 with pdf.
Table of Contents
MP Board Class 10 Math Exercise 6.1 Solution
1. Fill in the blanks using the correct word given in brackets:
(i) All circles are …………. (congruent, similar)
(ii) All squares are ……………… (similar, congruent)
(iii) All ……………… triangles a’e similar. (isosceles, equilateral)
(iv) Two polygons of the same number of sides are similar, if (a) their corresponding angles are …………. and (b) their corresponding side are …………………. (equal, proportional)
Solutions. (i) Similar, (ii) Similar, (iii) Equilateral, (iv) (a) equal (b) proportional
2. Give two different examples of pair of
(i) similar figures.
Solution: Coin, wheel of a cart
(ii) non-similar figures.
Solution:
A square Rhombus
3. State weather the following quadrilaterals are similar or not:
Solution: (Not Similar) On observing the given figures, we find that
Their corresponding sides are proportional but their corresponding angles are not equal.
∴ The given figures are not similar.
10th Maths Exercise 6.1 Illustrative Examples
Example 1. A and B are respectively the points on the sides PQ and PR of a ∆PQR such that PQ = 12.5 cm, PA = 5 cm, BR = 6 cm and PB = 4 cm. Is AB || QR? Give reason.
Solutions:
\[\frac{PA}{AQ}=\frac{PB}{BR}=\frac{2}{3}\]
AB || QR
Example 2. In the given fig. DE || BC. If AD=X, DB=x-2, AE =X+2 and EC=X-1, find the value of x.
Solution: In ∧ABC, we have
DE || BC,
\[\frac{AD}{DB}=\ \frac{AE}{EC}\ \left(by\ BPT\right)\]
\[\frac{x}{x-2}=\frac{x+2}{x-2}\]
\[x^2-x=x^2-4\]
x=4
Triangles Introduction
You are already aware with the term “congruent”. It means two figures or objects having same shape and size. For e.g. two coins of one rupee. In this chapter we will study about similar triangles, two figures or objects are said to be similar if they have same shape but not necessarily same size. Note: All congruent figures are similar but all similar figures need not be congruent.
Two polygons of the same number of sides are similar, if (1) their corresponding angles are equal (ii) their corresponding sides are in the same ratio (proportion).
If quadrilateral A’B’C’D’ is similar to ABCD then
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