Congruence of Triangles Test

Result

Congruence of Triangles Test - 3

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Question 1
1 / -0

Three students A, B and C write 3 statements.

A writes ''Congruent triangles are always equal in size.''
B writes ''All similar triangles are congruent.''
C writes ''If two triangles are equal, then their corresponding sides are equal.''

Who write(s) an incorrect statement?

A
A

B
B

C
C

D
All of them

Solution

If two triangles are similar, then it is not always true that they are congruent.

Similarity means that they are equal in shape but not always in size.
Question 2
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Which of the following statements is correct?

Statement I: If two pairs of sides of two triangles are equal in length, and the included angles are equal in measurement, then the triangles are congruent.
Statement II: If two pairs of angles of two triangles are equal in measurement, and the included sides are equal in length, then the triangles are congruent.

A
Only statement I

B
Only statement II

C
Both statements I and II

D
Neither statement I nor statement II

Solution

Both the statements are true

If two pairs of sides of two triangles are equal in length, and the included angles are equal in measurement, then the triangles are congruent. It is called SAS criterion.

If two pairs of angles of two triangles are equal in measurement, and the included sides are equal in length, then the triangles are congruent. It is called ASA criterion.
Question 3
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Which of the following statements is TRUE?

A
If two isosceles triangles have one angle in common, then these are congruent triangles.

B
If sides of two triangles are not equal, then they are congruent.

C
If sides of two triangles are equal. then they are congruent by HL rule.

D
If all angles are equal in a triangle, then they are congruent by SSS rule.

Solution

If two isosceles triangles have one angle in common, then these are congruent triangles.
(By SAS rule)