Triangles Test

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Triangles Test - 25

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Weekly Quiz Competition

Question 1
1 / -0

In the figure, $$AD$$ and $$BC$$ are perpendicular to $$AB$$, and $$AD=BC$$. Then , by $$SAS$$ congruence postulate, $$\displaystyle \Delta ABC\cong $$

A
$$\displaystyle \Delta ABD$$

B
$$\displaystyle \Delta BDA$$

C
$$\displaystyle \Delta BAD$$

D
$$\displaystyle \Delta ADB$$

Solution

$$AD\perp AB$$ and $$BC\perp AB$$ [ Given ]

$$\therefore$$ $$\angle BAD=\angle ABC=90^o$$ ---- ( 1 )

In $$\triangle ABC$$ and $$\triangle BAD$$

$$BC=AD$$ [ Given ]
$$\angle ABC=\angle BAD=90^0$$ [ From ( 1 ) ]
$$AB=BA$$ [ Common side ]

$$\therefore$$ $$\triangle ABC\cong\triangle BAD$$
Question 2
1 / -0

Which of the following statements is true when $$\displaystyle \Delta ABC\cong \Delta DEF.$$

A
$$\displaystyle \angle A=\angle D$$

B
$$\displaystyle \angle A=\angle E$$

C
$$\displaystyle \angle A=\angle F$$

D
none of these

Solution

Given $$\triangle ABC \cong \triangle DEF$$.

Then the corresponding parts will also be equal.

That is by CPCT rule, corresponding parts of congruent triangles are equal.

Then, $$AB=DE$$, $$BC=EF$$, $$AC=DF$$, $$\angle A=\angle D$$, $$\angle B=\angle E$$ and $$\angle C=\angle F$$.

Thus, $$\angle A=\angle D$$.
Hence, option $$A$$ is correct.
Question 3
1 / -0

When two triangles have corresponding sides equal in length, then the two triangles are congruent.

A
SAS congruency Theorem

B
AA congruency Theorem

C
AAA congruency Theorem

D
SSS congruency Theorem

Solution

All $$3$$ sides of a triangle are equal with all $$3$$ sides of another triangle then these two triangles are said to be congruent SSS congruency Theorem.
Therefore, D is the correct answer.
Question 4
1 / -0

By $$SAS$$ congruence rule, $$\triangle PQR$$ is congruent to

A
$$\triangle BCA$$

B
$$\triangle CAB$$

C
$$\triangle ABC$$

D
$$\triangle ACB$$

Solution

In $$\triangle PQR$$ and $$\triangle CAB,$$

$$PQ=CA$$ [given]
$$PR=CB$$ [given]
and, $$\angle QPR=\angle ACB$$ [given]

Thus, by $$SAS$$ congruence rule,
$$\triangle PQR \cong \triangle CAB$$

Hence, $$Op-B$$ is correct.
Question 5
1 / -0

Which pair of triangles shows congruency by the SSS postulate?

A
figure C

B
figure A

C
figure B

D
figure D

Solution

From figure C, triangles are congruent by the SSS postulate because the three sides of one triangle are congruent to three sides of another triangle.
Therefore, the given triangles are congruent by the SSS congruency postulate.
Question 6
1 / -0

Which of the following can be used to prove that $$\Delta ABC \cong \Delta SRT$$?

A
ASA

B
SAS

C
RHS

D
AAA

Solution

Two triangles triangle are congruent, if the hypotenuse and one side of the one triangle are respectively equal to the hypotenuse and one side of the other.
Therefore, $$\Delta ABC \cong \Delta SRT$$ by RHS congruence condition.
Question 7
1 / -0

In $$\displaystyle \Delta ABC, AB=5 \ cm, BC=4 \ cm$$ and $$AC=8 \ cm.$$ The smallest angle is .......... and the greatest angle is ..........

A
$$\displaystyle \angle A,\angle B$$

B
$$\displaystyle \angle B,\angle A$$

C
$$\displaystyle \angle A,\angle C$$

D
$$\displaystyle \angle B,\angle C$$

Solution

In $$\displaystyle \Delta ABC,$$ $$BC$$ is the smallest side and $$AC$$ is the greatest side. Hence, $$\displaystyle \angle A$$ is the smallest angle and $$\displaystyle \angle B$$ is the greatest angle.
Question 8
1 / -0

What is the largest side of the triangle?

A
$$\overline{AB}$$

B
$$\overline{BC}$$

C
$$\overline{CA}$$

D
$$\overline{AC}$$

Solution

In $$\triangle ABC,$$ $$\angle B$$ is equal to $$90^o$$ which implies that the $$\triangle ABC$$ is a right-angled triangle, and in a right angle triangle side opposite to the right angle is the largest.
Because the right angle is the biggest among all three angles of the triangle.
Question 9
1 / -0

In a triangle, the difference of any two sides is ____ than the third side.

A
Smaller

B
Equal

C
Greater

D
None of these

Solution

In a triangle, the difference of any two sides is smaller than the third side.
Question 10
1 / -0

If three sides of a triangle are equal to three sides of another triangle, then the two triangles are congruent. This is _____ condition for congruence.

A
$$ASA$$

B
$$AAS$$

C
$$SSS$$

D
$$SAS$$

Solution

Side-Side-Side $$(S.S.S)$$ condition states that if three sides of one triangle are equal to three sides of another triangle then the two triangles are congruent.