CBSE Class 10 Maths Notes Chapter 11 Constructions
Neha Tanna22 Apr, 2024
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CBSE Class 10 Maths Notes Chapter 11: These are the class 10 maths notes for the topic "Constructions." The revision of concepts for the CBSE Class 10 Board Exams is aided by these notes.
This article will go into detail on how to construct the line segment division, how to construct tringles using the scale factor, and how to construct tangents to a circle with two separate scenarios. Read the article below to find out more.CBSE Class 10 Maths Notes Chapter 11 PDF
The chapter on "Constructions" in mathematics class 10 is crucial. Students can use the notes and solutions for this chapter to learn and comprehend Constructions for class 10. The entire chapter, including the answers to the questions that remain unanswered, has been made available in PDF format for the benefit of the students.CBSE Class 10 Maths Notes Chapter 11 PDF
CBSE Class 10 Maths Notes Chapter 11
Dividing a Line Segment
Bisecting a Line Segment
Step 1: Draw arcs that are centred at both ends of the line segment and cross on either side, using a radius greater than half the length of the line segment. Step 2: Connect the intersecting points. The line segment connecting the places of junction divides the line segment in half.
2) Given a line segment AB, divide it in the ratio
m:n
, where both m and n are positive integers.
Suppose we want to divide AB in the ratio 3:2 (m=3, n=2)
Step 1 : Draw any ray A X , making an acute angle with line segment A B .
Step 2 : Locate 5 (= m + n) points A 1 , A 2 , A 3 , A 4 a n d A 5 on AX such that A A 1 = A 1 A 2 = A 2 A 3 = A 3 A 4 = A 4 A 5
Step 3 : Join B A5. ( A ( m + n ) = A 5 )
Step 4 : Through point, A 3 ( m = 3 ) , draw a line parallel to B A 5 (by making an angle equal to ∠ A A 5 B ) at A 3 intersecting AB at point C.
Then, AC: CB = 3: 2.
Constructing Similar Triangles
Constructing a Similar Triangle with a Scale Factor
Suppose we want to construct a triangle whose sides are 3/4 times the corresponding sides of a given triangle. BB 3 /BB 4 = 3/4
Steps of Construction:
Step 1 : Draw any ray B X making an acute angle with side B C (on the side opposite to the vertex A).
Step 2 : Mark 4 consecutive distances(since the denominator of the required ratio is 4) on B X as shown.
Step 3 : Join B 4 C, as shown in the figure.
Step 4 : Draw a line through B 3 parallel to B 4 C to intersect BC at C’.
Step 5 : Draw a line through C’ parallel to AC to intersect AB at A’. Δ A ′ B C ′ is the required triangle.
The same procedure can be followed when the scale factor > 1. When building a triangle that resembles a given triangle using a particular scale factor, there are two scenarios. They are as follows:Case 1: The scale factor is less than 1 and the triangle that needs to be built is less than the triangle that is provided.
Case 2: The scale factor is bigger than 1 and the triangle that needs to be built is larger than the triangle that is provided.
In this case, the scale factor refers to the ratio between the sides of the given triangle and the sides that need to be produced for the triangle.CBSE Class 10 Syllabus 2024-25
Drawing Tangents to a Circle
Tangents: Definition
A tangent to a circle is a line which touches the circle at exactly one point .For every point on the circle, there is a unique tangent passing through it.
Number of tangents to a circle from a given point
i) If the point is in an interior region of the circle , any line through that point will be a secant. So, in this case, there is no tangent to the circle.
ii) When the point lies on the circle, there is accurately only one tangent to a circle.
iii) When the point lies outside of the circle, there are exactly two tangents to a circle.
Drawing tangents to a circle from a point outside the circle
To build the tangents from a location outside of a circle.
Let O be the centre of the circle, and P be the exterior point from which the tangents are to be drawn.
Step 1: Connect and divide the PO. Let M be PO's midpoint.
Step 2: Mark the circle's centre (M) and radius (MO or MP). At locations Q and R, let it cross the specified circle.
Step 3: Include PR and PQ
Step 4: The necessary tangents to the circle are PR and QQ.
Benefits of CBSE Class 10 Maths Notes Chapter 11
To obtain a more straightforward understanding of the ideas and principles involved in the creation of geometric forms, these notes for Class 10 Maths Constructions are perfect. Students will be able to concentrate on the key ideas and understand them more quickly. These notes will also serve as a guide for them as they practise and become proficient in geometric construction techniques.CBSE Class 10 Maths Notes Chapter 11 FAQs
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