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Any two of the four triangles formed by ...

Any two of the four triangles formed by joining the mid - points of the sides of a given triangle are :

A

congruent

B

equal in area but not congruent

C

unequal in area and not congruent

D

none of the above

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The correct Answer is:
To solve the problem of determining the relationship between any two of the four triangles formed by joining the midpoints of the sides of a given triangle, we can follow these steps: ### Step 1: Understand the Triangle and its Midpoints Consider a triangle ABC. Identify the midpoints of each side of the triangle. Let's denote the midpoints as D, E, and F, where: - D is the midpoint of side AB - E is the midpoint of side BC - F is the midpoint of side CA
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ARIHANT SSC-GEOMETRY-INTRODUCTORY EXERCISE - 12.2
  1. The triangle is formed by joining the mid point of the sides AB, BC an...

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  2. One side other than the hypotenuse of right angle isosceles triangle i...

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  3. Any two of the four triangles formed by joining the mid - points of th...

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  4. The internal bisectors of angleB and angleC of DeltaABC meet at O. If ...

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  5. The point in the plane of a triangle which is at equal perpendicular d...

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  6. Incentre of a triangle lies in the interior of :

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  7. In a triangle PQR, PQ = 20 cm and PR = 6 cm, the side QR is :

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  8. The four triangles formed by joining the pairs of mid - points of the ...

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  9. The circumference of the circle is 176m. Then the area of the circle i...

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  10. In a DeltaABC, a line PQ parallel to BC cuts AB at P and AC at Q. If B...

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  11. Sunil buys an article with 20% discount on its marked price. He makes ...

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  12. If D is such a point on the side, BC of DeltaABC that (AB)/(AC)=(BD)/(...

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  13. In right angled DeltaABC,angleB=90^(@), if P and Q are points on the ...

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  14. ABC is a right angle triangle at A and AD is perpendicular to the hypo...

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  15. If DeltaABC and DeltaDEF are so related the (AB)/(FD)=(BC)/(DE)=(CA)/(...

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  16. ABC is a right angle triangle at A and AD is perpendicular to the hypo...

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  17. Let ABC be an equilateral triangel. Let BE|CA meeting CA at E, then (A...

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  18. If D, E and F are respectively the mid - points of sides BC, AC and AB...

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  19. A triangle PQR is a right angled triangle at Q. E and F are the mid po...

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  20. ABC is a triangle and DE is drawn parallel to BC cutting the other sid...

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