CBSE Class 10 Sample Paper for 2025 Boards - Maths Standard
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CBSE Class 10 Sample Paper for 2025 Boards - Maths Standard
Last updated at Feb. 12, 2025 by Teachoo
This question is similar to Chapter 6 Class 10 Triangles - Ratio of Area of Similar Triangles
Please check the Question here
Transcript
Question 26 (A) In š„ABC, D, E and F are midpoints of BC,CA and AB respectively. Prove that ā³ š¹šµš· ā¼ ā³ DEF and ā³ DEF ā¼ ā³ ABC We know that line joining mid-points of two sides of a triangle is parallel to the 3rd side In ĪABC , F and E are mid-points of AB and AC resp., ā“ FE ā„ BC So, FE ā„ BD also Similarly, D and E are mid-points of BC and AC resp. ā“ DE ā„ AB So, DE ā„ BF also From (1) & (2) FE ā„ BD & DE ā„ BF Therefore, opposite sides of quadrilateral is parallel ā“ DBEF is a parallelogram Similarity, we can prove DCEF is a parallelogram Since DEBF is a parallelogram And, in parallelogram, opposite angles are equal ā“ ā DEF = ā ABC Similarly, Since DCEF is a parallelogram And, in parallelogram, opposite angles are equal ā“ ā DFE = ā ACB Proving ā³ DEF ā¼ ā³ ABC Now, In ĪDEF and ĪABC ā DFE = ā ACB ā DEF = ā ABC By using AA similarity criterion Ī DEF ā¼ Ī ABC Proving ā³ FBD ā¼ ā³ DEF We need to prove one more angle equal Since FE ā„ BC & FD can be the transversal ā EFD = ā BDF Now, In ĪFBD and ĪDEF ā FBD = ā DEF ā BDF = ā EFD By using AA similarity criterion Ī FBD ā¼ Ī DEF
