1 Marks Question

Question 511 Mark

In given pairs of triangles of Figure. applying only $ASA$ congruence criterion, determine which triangles are congruent. Also, write the congruent triangles in symbolic form.

Answer

$∆\text{ABD} ≅ ∆\text{CDB}$

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Question 521 Mark

Two angles are said to be, ________ if they have equal measures.

Answer

Two angles are said to be, congruent if they have equal measures.Solution:
Two angles are said to be congruent, if they have equal measures.

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Question 531 Mark

Measures of each of the angles of an equilateral triangle is ________.

Answer

Measures of each of the angles of an equilateral triangle is $60^\circ$ as all the angles in an equilateral triangle are equal. Let $x$ be the angle of equilateral. According to the angle sum property of a triangle.
$x + x + x = 180^\circ $
$\Rightarrow \ 3\text{x}={180^{\circ}}$
$\Rightarrow \ 3\text{x}=\frac{180^{\circ}}{3}$
$\Rightarrow \ \text{x}=60^{\circ}$

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Question 541 Mark

In the following pair of triangles of Figure. the lengths of the sides are indicated along the sides. By applying $SSS$ congruence criterion, determine which triangles are congruent. If congruent, write the results in symbolic form.

Answer

$\triangle\text{STU} \cong \triangle\text{PQR}$

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Question 551 Mark

Two acute angles are congruent.

Answer

False. Solution: Because the measure of two acute angles may be different.

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Question 561 Mark

In given pairs of triangles of Figure. applying only $ASA$ congruence criterion, determine which triangles are congruent. Also, write the congruent triangles in symbolic form.

Answer

Not possible, because the side is not included between two angles.

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Question 571 Mark

A one rupee coin is congruent to a five rupee coin.

Answer

False. Solution: Because they don’t have same shape and same size.

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Question 581 Mark

Answer

$\triangle\text{LMN} \cong \triangle\text{GHI}$

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Question 591 Mark

If the areas of two circles are the same, they are congruent.

Answer

True.
Solution:
Because areas of two circles will be equal only if their radii are equal and circle with same radii will superimpose to each other.

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Question 601 Mark

Every triangle has at least _________ acute angle (s).

Answer

Every triangle has atleast two acute angle (s). Solution: Every triangle has atleast two acute angles.

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Question 611 Mark

Answer

$\triangle\text{STU} \cong \triangle\text{SVU}$

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Question 621 Mark

If the areas of two rectangles are same, they are congruent.

Answer

False. Solution: Because rectangles with the different length and breadth may have equal areas. But, they will not superimpose to each other.

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Question 631 Mark

The ________ triangle always has altitude outside itself.

Answer

The obtuse triangle always has altitude outside itself. Solution: The obtuse angled triangle always has altitude outside itself.

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Question 641 Mark

$ABC$ is an isosceles triangle with $AB = AC$ and $D$ is the mid-point of base $BC$ Figure. Is $Δ\text{ABD} ≅ Δ\text{ACD}?$ If so why?

Answer

Given, $AB = AC$ and $BD = CD$ Yes, by SSS congruence criterion, $Δ\text{ABD} ≅ Δ\text{ACD}$

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Question 651 Mark

In Figure. $AB = AD$ and $\angle\text{BAC}=\angle\text{DAC}.$ then
$i. \triangle.........\cong\triangle\text{ABC}.$
$ii. \text{BC} =.................$
$iii. \angle\text{BCA}=..........$
$iv.$ Line segment $AC$ bisects $..........$ and $..........$

Answer

In $\triangle\text{ABC}$ and $\triangle\text{ADC},$
$\text{AB} = \text{AD} [$given$]$
$AC = AC [$common side$]$
$\angle\text{BAC}=\angle\text{DAC} [$given$]$
By $\ce{SAS}$ congruence criterion,
$\triangle\text{ADC}\cong\triangle\text{ABC}$
Now,$\text{ BC} =\text{ DC} [$by $\ce{CPCT}]$
Also, $\angle\text{BCA}=\angle\text{DCA} [$by $\ce{CPCT}]$
Line segment $AC$ bisects $\angle\text{BAD}$ and $\angle\text{BCD}.$
Since, $\angle\text{BAC}=\angle\text{DAC}$
and $\angle\text{BCA}=\angle\text{DCA}$

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Question 661 Mark

Sum of any two angles of a triangle is always greater than the third angle.

Answer

It is not necessary that sum of any two angles of a triangle is always greater than the third angle,
e.g. Let the angles of a triangle be $20^\circ , 50^\circ$ and $110^\circ ,$ respectively.
Hence, $20^\circ + 50^\circ = 70^\circ ,$ which is less than $110^\circ .$

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Question 671 Mark

If two legs of a right triangle are equal to two legs of another right triangle, then the right triangles are congruent.

Answer

True. Solution: If two legs of a right angled triangle are equal to two legs of another right angled triangle, then their third leg will also be equal. Hence, they will have same shape and same size.

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Question 681 Mark

If the areas of two squares is same, they are congruent.

Answer

True.
Solution:
Because two squares will have same areas only if their sides are equal and squares with same sides will superimpose to each other.

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Question 691 Mark

In given pairs of triangles of Figure. using only $RHS$ congruence criterion, determine which pairs of triangles are congruent. In case of congruence, write the result in symbolic form:

Answer

Not possible, because there is not any right angle.

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Question 701 Mark

In Figure.$AD \bot BC$ and $AD$ is the bisector of angle $BAC.$ Then, $\triangle\text{ABD} \cong\triangle\text{ACD}$ by $RHS.$

In $\triangle\text{ABD}$ and $\triangle\text{ACD},$
$\text{AD} = \text{AD}$ [common side] $\angle\text{BAD}=\angle\text{CAD}$
$[\because AD$ is the bisector of $\angle\text{BAC}]$ By $ASA$ congruence criterion, $\triangle\text{ABD}\cong\triangle\text{ACD}$

Answer

In $\triangle\text{ABD}$ and $\triangle\text{ACD},$
$\text{AD} = \text{AD}$ [common side]
$\angle\text{BAD}=\angle\text{CAD}$
$[\because AD$ is the bisector of $\angle\text{BAC}]$
By $ASA$ congruence criterion, $\triangle\text{ABD}\cong\triangle\text{ACD}$

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Question 711 Mark

In Figure. which pairs of triangles are congruent by $SAS$ congruence criterion (condition)? If congruent, write the congruence of the two triangles in symbolic form.

Answer

Not congruent, because angle is not included between two sides.

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Question 721 Mark

Two rectangles are congruent, if they have same ________ and _________.

Answer

Two rectangles are congruent, if they have same length and breadth. Solution: Two rectangles are congruent, if they have same length and breadth.

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Question 731 Mark

In given pairs of triangles of Figure. applying only $ASA$ congruence criterion, determine which triangles are congruent. Also, write the congruent triangles in symbolic form.

Answer

$∆\text{MNO} ≅ ∆\text{PON}$

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Question 741 Mark

In $\triangle\text{ABC}, AB = 3.5\ cm, AC = 5\ cm, BC = 6\ cm$ and in $\triangle\text{PQR},$ $PR= 3.5\ cm, PQ = 5\ cm, RQ = 6\ cm.$ Then $\triangle\text{ABC} \cong \text{PQR}.$

Answer

In $\triangle\text{ABC}$ and $\triangle\text{PRQ},$
$AB = PR = 3.5\ cm, BC = RQ = 6\ cm$ and $AC = PQ = 5\ cm$
By $SSS$ congruence criterion, $\triangle\text{ABC}\cong\triangle\text{PRQ}$

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Question 751 Mark

Two right angles are congruent.

Answer

True. Solution: Since, the measure of right angles is always same.

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Question 761 Mark

The difference between the lengths of any two sides of a triangle is smaller than the length of third side.

Answer

The difference between the lengths of any two sides of a triangle is smaller than the length of third side. $AB - BC < AC$

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Question 771 Mark

If hypotenuse and an acute angle of one right triangle are equal to the hypotenuse and an acute angle of another right triangle, then the triangles are congruent.

Answer

In $\triangle\text{ABC}$ and $\triangle\text{PQR},$
$\angle\text{B}=\angle\text{Q}=90^{\circ}$
$\angle\text{C}=\angle\text{R}$ [given] $\angle\text{A}=\angle\text{P}$
Now, In $\triangle\text{ABC}$ and $\triangle\text{PQR},$
$\angle\text{A}=\angle\text{P}$
$\text{AC} =\text{ PR}$
$\angle\text{C}=\angle\text{R}$
By $ASA$ congruene criterian, $\triangle\text{ABC}\cong\triangle\text{PQR}$

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Question 781 Mark

It is possible to have a right-angled equilateral triangle.

Answer

In a right angled triangle, one angle is equal to $90^\circ$ and in equilateral triangle, all angles are equal to $60^\circ .$

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Question 791 Mark

Two circles having same circumference are congruent.

Answer

True.
Solution:
If two circles have same circumference, then their radii will be equal. Hence, the circles will superimpose to each other.

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Question 801 Mark

In a triangle, sum of squares of two sides is equal to the square of the third side.

Answer

False. Solution: Only in a right angled triangle, the sum of two shorter sides is equal to the square of the third side.

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Question 811 Mark

Without drawing the triangles write all six pairs of equal measures in each of the following pairs of congruent triangles. $\triangle\text{STU} \cong \triangle\text{DEF}$

Answer

We know that, corresponding parts of congruent triangles are equal. $\triangle\text{STU} \cong \triangle\text{DEF}$ $\angle\text{S}=\angle\text{D},\angle\text{T}=\angle\text{E}$ and $\angle\text{U}=\angle\text{F},\text{ST}=\text{DE},\text{TU}=\text{EF}$ and $\text{SU}=\text{DF}$

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Maths 1 Marks Question