Tag: mid-point and its converse

Questions Related to mid-point and its converse

The straight line joining the mid-points of the opposite sides of a parallelogram divides it into two parallelogram of equal area  

maths mid-point and its converse proving the mid-point theorem the mid-point theorem mid point theorem

  1. True

  2. False

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Correct Option: A

In a $\triangle DEF$; $A,B$ and $C$ are the mid-points of $EF,FD$ and $DE$ respectively. If the area of $\triangle DEF$ is $14.4{ cm }^{ 2 }$, then find the area of $\triangle {ABC}$.

maths mid-point and its converse proving the mid-point theorem the mid-point theorem mid point theorem

  1. $1.75$cm

  2. $2.54$cm

  3. $3.2$cm

  4. $3.6$cm

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Correct Option: D
Explanation:

Fact: Using mid-point theorem $\dfrac{\Delta{DEF}}{\Delta{ABC}}=4$


Here $\Delta{DEF}=14.4$ cm$^2$ is given 
Hence are of triangle $ABC $ is given by $ \dfrac{14.4}{4}=3.6$ cm$^2$ 

In a $\triangle ABC$, if $D, E, F$ are the midpoints of the sides $BC, CA, AB$ respectively then $\overline {AD} + \overline {BE} + \overline {CF} =$

maths mid-point and its converse proving the mid-point theorem the mid-point theorem mid point theorem

  1. $\overline {0}$

  2. $\overline {AE}$

  3. $\overline {BD}$

  4. $\overline {CE}$

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Correct Option: A

A cross section at the midpoint of the middle piece of a human sperm will show

maths mid-point and its converse proving the mid-point theorem the mid-point theorem mid point theorem

  1. Centriole, mitochondria and 9 +2 arrangement of microtubules.

  2. Centriole and mitochondria

  3. Mitochondria and 9+2 arrangement of microtubules.

  4. 9+2 arrangement of microtubules only.

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Correct Option: C
Explanation:

The middle piece is the tubular structure in which mitochondria are spirally arranged and it also has the beginning part of the flagellum. The sperm tail or the flagellum is based upon unique 9+2 arrangement. This arrangement refers to the nine peripheral, symmetrically arranged microtubule doublets.
Thus, the cross-section of the middle piece of sperm will show mitochondria and 9+2 arrangement of microtubules.
Hence, the correct answer is option (C), 'Mitochondria and 9+2 arrangement of microtubules'.