1 Marks Question

Question 11 Mark

Can all the four angles of a quadrilateral be obtuse angles? Give reason for your answer.

Answer

No, because then the sum of four angles of the quadrilateral will be more than $360^{\circ}$ whereas sum of four angles of a quadrilateral is always equal to $360^{\circ}$.

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Question 21 Mark

Diagonals of a parallelogram are perpendicular to each other. Is this statement true? Give reason for your answer.

Answer

This statement not true. Diagonals of a parallelogram bisect each other.

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Question 31 Mark

$D, E$ and $F$ are the mid-points of the sides $BC, CA$ and $AB,$ respectively of an equilateral triangle $ABC.$ Show that $\Delta\text{DEF}$ is also an equilateral triangle.

Answer

Given In equilateral $\Delta\text{ABC}, D, E$ and $F$ are the mid-points of sides $BC, CA$ and $AB,$ respectively.To show $\Delta\text{DEF}$ is an equilateral triangle.

Proof Since in $\Delta\text{ABC}, E$ and $F$ are the mid-points of $AC$ and $AB$ respectively, then $EF || BC$
and $\text{EF}=\frac{1}{2}\text{BC}\ ...(\text{i})$
$DF || AC, DE || AB$
$\text{DE}=\frac{1}{2}\text{AB}$ and $\text{FD}=\frac{1}{2}\text{AC} [$by mid-point theorem$] …(ii)$
since $\Delta\text{ABC}$ is an equilateral triangle
$AB = BC = CA$
$\Rightarrow\ \frac{1}{2}=\frac{1}{2}\text{BC}=\frac{1}{2}\text{CA}[$ dividing by $2]$
$\Rightarrow\ \therefore\ \text{DE}=\text{EF}=\text{FD} [$from Eqs. $(i)$ and $(ii)]$
Thus, all sides of $ADEF$ are equal.
Hence, $\Delta\text{DEF}$ is an equilateral triangle.
Hence proved.

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Question 41 Mark

Diagonals of a rectangle are equal and perpendicular. Is this statement true? Give reason for your answer.

Answer

The given statement is not true. Diagonals of a rectangle need not to be perpendicular.

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Question 51 Mark

Can all the angles of a quadrilateral be right angles? Give reason for your answer.

Answer

Yes, all the angles of a quadrilateral can be right angles. In this case, the quadrilateral becomes rectangle or square.

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