Triangles Test

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Triangles Test - 26

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Weekly Quiz Competition

Question 1
1 / -0

If the hypotenuse and one of the other two sides of a right angles triangle is equal to the hypotenuse and one of the other two sides of the other right-angled triangle respectively, then the two right-angled triangles are ___.

A
congruent

B
unequal

C
equilateral

D
None of the these

Solution

Given,
Both the hypotenuse of the triangles are equal
One of other two sides are equal
Both are right angled triangles.
So by Side Angle Side we can say that both the angles are congruent.
Hence option A is the correct answer.
Question 2
1 / -0

AC is a diagonal of a rectangle ABCD. Which triangle is congruent to $$\triangle$$ ADC?

A
$$\triangle BCA$$

B
$$\triangle ACB$$

C
$$\triangle CBA$$

D
$$\triangle BCD$$

Solution

In $$\triangle ADC$$ and $$\triangle CBA$$,

$$AD=CB$$ (Opposite sides of rectangle)

$$DC=BA$$ (Opposite sides of the rectangle)

$$AC=CA$$ (Common side)

$$\triangle ADC\cong \triangle CBA$$ by $$SSS$$ criteria.

So option $$C$$ is correct.
Question 3
1 / -0

In $$\triangle$$ ABC, $$AB = 5$$ cm, $$BC= 6$$ cm and $$CA= 7$$ cm. Identify the relation between the angles.

A
$$\angle B > \angle A > \angle C$$

B
$$\angle A > \angle B > \angle C$$

C
$$\angle B > \angle C > \angle A$$

D
$$\angle C > \angle A > \angle B$$

Solution

In any triangle angle opposite to the longer side is larger.
Here $$CA$$ is the longest side and angle opposite to it is $$\angle B$$.
So $$\angle B$$ is largest angle.
Then comes $$BC$$ and angle opposite to it is $$\angle A$$
So angle $$A$$ is second largest.
Then comes $$AB$$ angle opposite to it is $$\angle C$$
So $$\angle C$$ is smallest.
So the decreasing order of angles is
$$\angle B>\angle A>\angle C$$
Question 4
1 / -0

In $$\Delta JKL$$ and $$\Delta MNO$$, $$\displaystyle { JL } \cong { ON } $$ and $$\displaystyle { KL } \cong { OM } $$, then the condition which will make both triangles congruent is:

A
$$\displaystyle \angle L\cong \angle O$$

B
$$\displaystyle \angle K\cong \angle M$$

C
$$\displaystyle \angle J\cong M$$

D
$$\displaystyle \angle J\cong \angle N$$

Solution

Two triangles can be congruent by the SAS test, since here we are equating two sides and one angle.
For the SAS test of congruency, the condition is that the angle must be included between the two sides to ensure correctness of the test.
Similarly, here the two included angles must be congruent for the triangles to be congruent.
They are $$\angle L \cong \angle O$$ since they are the included angles of sides $$JL-KL$$ and $$ON-OM$$ respectively.
Question 5
1 / -0

In $$\triangle ABC$$ and $$\triangle DEF$$, $$\angle B=\angle E,AB=DE,BC=EF$$. The two triangles are congruent under ............. axiom.

A
SSS

B
AAA

C
SAS

D
ASA

Solution

Two sides and included angle of $$\triangle ABC$$ and $$\triangle DEF$$ are equal.
Therefore the triangles are congruent by $$SAS$$ axiom.
Option $$C$$ is correct.
Question 6
1 / -0

Which of the following is congruent to the above figure?

A

B

C

D
None of these

Solution

Two figures are said to be congruent if they have exactly same shape and size or one can exactly overlap the other.
Here, if we rotate the figure in option $$C$$, and place it over each other, we get the same figure given, i.e. they will overlap.

Therefore, option $$C$$ is correct.
Question 7
1 / -0

Which of the following is congruent to the above figure?

A

B

C

D
None of these

Solution

Two figures are said to be congruent if they have exactly same shape and size or one can exactly overlap the other.
Here, if we rotate the figure in option $$A$$, and place it over each other, we get the same figure given, i.e. they will overlap.

Therefore, option $$A$$ is correct.
Question 8
1 / -0

Which of the following sides are equal if $$\angle RPQ$$ and $$\angle RQP$$ are similar?

A
$$RP=RQ$$

B
$$RP=PQ$$

C
$$RQ=PQ$$

D
None of these

Solution

Here, since two angles of the triangle are equal, the $$\triangle RPQ $$ is an isosceles triangle.

Then, from the converse of isosceles angle property,
sides opposite to equal angles of a triangle are equal.
Here, $$RP$$ is the side opposite to $$\angle RQP$$
and $$RQ$$ is the side opposite to $$\angle RPQ$$.

Thus, if $$\angle RPQ=\angle RQP$$, then $$RP=RQ$$ .

Therefore, option $$A$$ is correct.
Question 9
1 / -0

Two plane figures are said to be congruent if they have_____.

A
same size

B
same shape

C
same size and same shape

D
none

Solution

Two plane figures are congruent to each other, if trace copy of one of the figures covers the other figure completely.

Therefore, option $$C$$ is correct.
Question 10
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A triangle with two congruent sides and congruent base angles is termed as?

A
Equilateral triangle

B
Isosceles triangle

C
Scalene triangle

D
None of these

Solution

A triangle with two congruent sides and congruent base angles is termed as an isosceles triangle.

If two sides of a triangle are congruent, then by isosceles triangle property, the angles opposite to these sides are congruent.
That is, base angles of the triangle are congruent.

Then, such a triangle is known as Isosceles triangle.

Therefore, option $$B$$ is correct.