1 Mark Question

Question 11 Mark

By applying SAS congruence condition, state which of the following pairs of triangle are congruent. State the result in symbolic form.

Answer

We have OA = OC, OB = OD and
$\angle\text{AOB}=\angle\text{COD}$ which are vertically opposite angles. Therefore by SAS condition,$\triangle\text{AOC}\cong\triangle\text{BOD}$

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Question 21 Mark

Fill in the blanks:
Two rectangles are congruent if .

Answer

Two rectangles are congruent if their lengths are equal and their breadths are also equal. The opposite sides of a rectangle are equal. So if two rectangles have lengths of the same size and breadths of the same size, then they are congruent to each other.

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Question 31 Mark

In $\triangle\text{ABC},$ it is known that $\angle\text{B}=\text{C}$. Imagine you have another copy of $\triangle\text{ABC}$.
Is $\triangle\text{ACB}\cong\triangle\text{ACB}?$

Answer

Yes $\triangle\text{ABC}\cong\triangle\text{ACB}$.

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Question 41 Mark

State the condition by which the following pairs of triangles are congruent.

Answer

AD = BC and $\angle\text{DAC}=\angle\text{BCA}$
Therefore, by SAS condition $\triangle\text{ABC}\cong\triangle\text{ADC}$.

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Question 51 Mark

Following statement are true or false;
If two triangles are equal in area, they are congruent.

Answer

False.
Solution:
Area of a triangle = 12 × base × height
Two triangles can have the same area but the lengths of their sides can vary and hence they cannot be congruent.

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Question 61 Mark

$\triangle\text{ABC}$ is isosceles with AB = AC. AD is the altitude from A on BC.
Is $\triangle\text{ABD}\cong\triangle\text{ACD}?$

Answer

Yes, $\triangle\text{ABD}\cong\triangle\text{CBD}$ by RHS congruence condition.

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Question 71 Mark

In $\triangle\text{ABC},$ it is known that $\angle\text{B}=\text{C}$. Imagine you have another copy of $\triangle\text{ABC}$.
Is it true to say that AB = AC?

Answer

Yes it is true to say that AB = AC since $\angle\text{ABC}=\angle\text{ACB}$.

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Question 81 Mark

$\triangle\text{ABC}$ is isosceles with AB = AC. AD is the altitude from A on BC.
Is it true to say that BD = DC?

Answer

Yes, it is true to say that BD = DC (C.P.C.T.) since we have already proved that the two triangles are congruent.

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Question 91 Mark

$\triangle\text{ABC}$ is isosceles with AB = AC. Line segment AD bisects $\angle\text{A}$ and meets the base BC in D.
Is it true to say that BD = DC?

Answer

Now, $\triangle\text{ABD}\cong\triangle\text{ACD}$ therefore by c.p.c.t., BD = DC.

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Question 101 Mark

By applying SAS congruence condition, state which of the following pairs of triangle are congruent. State the result in symbolic form.

Answer

We have BD = DC and
$\angle\text{ADB}=\angle\text{ADC}=90^\circ$
Therefore, by SAS condition $\triangle\text{ADB}\cong\triangle\text{ADC}$.

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Question 111 Mark

By applying SAS congruence condition, state which of the following pairs of triangle are congruent. State the result in symbolic form.

Answer

We have AB = DC and
$\angle\text{ABD}=\angle\text{CDB}$
Therefore, by SAS condition $\triangle\text{ABD}\cong\triangle\text{CBD}$.

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Question 121 Mark

State the condition by which the following pairs of triangles are congruent.

Answer

AC = BD, AD =BC and AB = BA
Therefore, by SAS condition $\triangle\text{ABD}\cong\triangle\text{BAC}$.

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Question 131 Mark

In $\triangle\text{ABC},$ it is known that $\angle\text{B}=\text{C}$. Imagine you have another copy of $\triangle\text{ABC}$.
State the three pairs of matching parts you have used to answer (i).

Answer

We have used $\angle\text{ABC}=\angle\text{ACB}$ and $\angle\text{ACB}=\angle\text{ABC}$ again.
Also BC = CB

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Question 141 Mark

$\triangle\text{ABC}$ is isosceles with AB = AC. Line segment AD bisects $\angle\text{A}$ and meets the base BC in D.
Is $\triangle\text{ADB}\cong\triangle\text{ADC}?$

Answer

We have AB = AC (Given)
$\angle\text{BAD}=\angle\text{CAD}$ (AD bisects $\angle\text{BAC}$ )
Therefore by SAS condition of congruence, $\triangle\text{ABD}\cong\triangle\text{ACD}$

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Question 151 Mark

Following statement are true or false;
If two squares have equal areas, they are congruent.

Answer

True.Solution:
Area of a square = side × side
Therefore, two squares that have the same area will have sides of the same lengths. Hence they will be congruent.

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Question 161 Mark

Fill in the blanks:
Two angles are congruent if .

Answer

Two angles are congruent if their measures are the same. On superposition, we can see that the angles are equal.

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Question 171 Mark

Fill in the blanks:
Two squres are congruent if .

Answer

Two squres are congruent if their sides are equal. All the sides of a square are equal and if two squares have equal sides, then all their sides are of the same length. Also angles of a square are $90^{\circ}$ which is also the same for both the squares.

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Question 181 Mark

Fill in the blanks:
Two line segments are congruent if .

Answer

Two line segments are congruent if they have the same length, since they can superpose on each other.

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Question 191 Mark

Which of the following pairs of triangle are congruent by ASA condition?

Answer

We have only BC = QR but none of the angles of $\triangle\text{ABC} $ and $\triangle\text{PQR}$ are equal.
Therefore, $\triangle\text{ABC}\ncong\triangle\text{PQR}$.

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Question 201 Mark

By applying SAS congruence condition, state which of the following pairs of triangle are congruent. State the result in symbolic form.

Answer

We have BC = QR,
$\angle\text{ABC}=\angle\text{PQR}=90^\circ$ and AB = PQ
Therefore, by SAS condition $\triangle\text{ABC}\cong\triangle\text{PQR}$.

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Question 211 Mark

State the condition by which the following pairs of triangles are congruent.

Answer

AB = AD and $\angle\text{BAC}=\angle\text{DAC}$
Therefore, by SAS condition $\triangle\text{BAC}\cong\triangle\text{DAC}$.

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Question 221 Mark

State the condition by which the following pairs of triangles are congruent.

Answer

AB = AD, BC =CD and AC = CA
Therefore, by SAS condition $\triangle\text{ABC}\cong\triangle\text{ADC}$.

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Question 231 Mark

$\triangle\text{ABC}$ is isosceles with AB = AC. AD is the altitude from A on BC.
State the pairs of matching parts you have used to answer (i).

Answer

We have used,
hypotenuse AB = hypotenuse AC
AD = DA
and $\angle\text{ADB}=\angle\text{ADC}=90^\circ$ ($\text{AD}\perp\text{BC}$ at point D)

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Question 241 Mark

Following statement are true or false;
All squares are congruent.

Answer

False.
Solution:
All the sides of a square are of equal length.
However, different squares can have sides of different lengths. Hence all squares are not congruent.

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Question 251 Mark

Fill in the blanks:
Two circles are congruent if .

Answer

Two circles are congruent if their radii are of the same length. Then the circles will have the same diameter and thus will be congruent to each other.

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Question 261 Mark

Following statement are true or false;
If two rectangles have equal area, they are congruent.

Answer

False. Solution:Area of a rectangle = length x breadth
Two rectangles can have the same area. However, the lengths of their sides can vary and hence they are not congruent.
Example: Suppose rectangle 1 has sides 8m and 8m and area 64 meter square. Rectangle 2 has sides 16m and 4m and area 64 meter square. Then rectangle 1 and 2 are not congruent.

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Question 271 Mark

In figure, $\triangle\text{ABC}$ is isosceles with AB = AC. State if $\triangle\text{ABC}\cong\triangle\text{ACB}.$ If yes, state three relations that you use to arrive at your answer.

Answer

Yes, $\triangle\text{ABC}\cong\triangle\text{ACB}$ by SSS condition.
Since, ABC is an isosceles triangle, AB = BC, BC = CB and AC = AB.

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Question 281 Mark

$\triangle\text{ABC}$ is isosceles with AB = AC. Line segment AD bisects $\angle\text{A}$ and meets the base BC in D.
State the three pairs of matching parts used to answer (i).

Answer

We have used AB, AC; $\angle\text{BAD}=\angle\text{CAD}$; AD, DA.

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