CBSE Class 10 Constructions Important Formulas and concepts for exams

CBSE Class 10 Constructions Important Formulas and concepts for exams. There are many more useful educational material which the students can download in pdf format and use them for studies. Study material like concept maps, important and sure shot question banks, quick to learn flash cards, flow charts, mind maps, teacher notes, important formulas, past examinations question bank, important concepts taught by teachers. Students can download these useful educational material free and use them to get better marks in examinations.  Also refer to other worksheets for the same chapter and other subjects too. Use them for better understanding of the subjects.

To construct a triangle similar to a given triangle as per given scale factor.

Example 1 - Construct a triangle similar to a given triangle ABC with its sides equal to 3/ 4 of the corresponding sides of the triangle ABC (i.e., of scale factor 3 /4).

Steps of Construction :

* Draw any ray BX making an acute angle with BC on the side opposite to the vertex A.

* Locate 4 (the greater of 3 and 4 in 3/4) points B₁, B₂, B₃ and B₄ on BX so that BB₁ = B₁B₂ = B₂B₃ = B₃B₄.

* Join B₄C and draw a line through B₃ (the 3rd point, 3 being smaller of 3 and 4 in 3 /4) parallel to B₄C to intersect BC at C′.

* Draw a line through C′ parallel to the line CA to intersect BA at A′ (see below figure).

Then, Δ A′BC′ is the required triangle.

Example 2 : Construct a triangle similar to a given triangle ABC with its sides equal to 5 /3 of the corresponding sides of the triangle ABC (i.e., of scale factor 5 /3).

Steps of Construction :

* Draw any ray BX making an acute angle with BC on the side opposite to the vertex A.

* Locate 5 points (the greater of 5 and 3 in 5/3) B₁, B₂, B₃, B₄ and B₅ on BX so that BB₁ = B₁B₂ = B₂B₃ = B₃B₄ = B₄B₅. 

* Join B₃(the 3rd point, 3 being smaller of 3 and 5 in 5 /3 ) to C and draw a line through B5 parallel to B₃C, intersecting the extended line segment BC at C′.

* Draw a line through C′ parallel to CA intersecting the extended line segment BA at A′ (see the below figure).

Then A′BC′ is the required triangle.

To construct the tangents to a circle from a point outside it.

Given : We are given a circle with centre ‘O’ and a point P outside it. We have to construct two tangents from P to the circle.

Steps of construction :

* Join PO and draw a perpendicular bisector of it. Let M be the midpoint of PO.

* Taking M as centre and PM or MO as radius, draw a circle. Let it intersect the given circle at the points A and B.

* Join PA and PB.

Then PA and PB are the required two tangents.

To Construct a tangent to a circle at a given point when the centre of the circle is known.

We have a circle with centre ‘O’ and a point P anywhere on its circumference. Then we have to construct a tangent through P.

Steps of Construction :

* Draw a circle with centre ‘O’ and mark a point ‘P’ anywhere on it. Join OP.

* Draw a perpendicular line through the point P and name it as XY, as shown in the figure.

* XY is the required tangent to the given circle passing through P.

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