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Examples

Example 1
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Example 2 Important Deleted for CBSE Board 2024 Exams

Construction 11.1 Important Deleted for CBSE Board 2024 Exams

Construction 11.2 Deleted for CBSE Board 2024 Exams

Construction 11.3 Important Deleted for CBSE Board 2024 Exams

How to construct Tangents to circle if center of circle is not given? Important Deleted for CBSE Board 2024 Exams

Constructions

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Last updated at May 29, 2023 by Teachoo

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). Here, we are given Ξ ABC, and scale factor 3/4 β΄ Scale Factor < 1 We need to construct triangle similar to Ξ ABC Letβs follow these steps Steps of construction Draw any ray BX making an acute angle with BC on the side opposite to the vertex A. Mark 4 (the greater of 3 and 4 in 3/4 ) points π΅_1,π΅_2,π΅_3 and π΅_4 on BX so that γπ΅π΅γ_1=π΅_1 π΅_2=π΅_2 π΅_3=π΅_3 π΅_4. Join π΅_4C and draw a line through π΅_3 (the 3rd point, 3 being smaller of 3 and 4 in 3/4) parallel to π΅_4 πΆ, to intersect BC at Cβ². 4. Draw a line through Cβ² parallel to the line CA to intersect BA at Aβ². Thus, Ξ Aβ²BCβ² is the required triangle Justification Since scale factor is 3/4, we need to prove (π¨^β² π©)/π¨π©=(π¨^β² πͺ^β²)/π¨πͺ=(π©πͺ^β²)/π©πͺ =π/π. By construction, BC^β²/π΅πΆ=(π΅π΅_3)/(π΅π΅_4 )=3/4. Also, AβCβ is parallel to AC So, they will make the same angle with line BC β΄ β AβCβB = β ACB Now, In Ξ AβBCβ and Ξ ABC β B = β B β AβCβB = β ACB Ξ AβBCβ βΌ Ξ ABC Since corresponding sides of similar triangles are in the same ratio (π΄^β² π΅)/π΄π΅=(π΄^β² πΆ^β²)/π΄πΆ=(π΅πΆ^β²)/π΅πΆ So, (π¨^β² π©)/π¨π©=(π¨^β² πͺ^β²)/π¨πͺ=(π©πͺ^β²)/π©πͺ =π/π. Thus, our construction is justified