# Free Congruence of Triangles 01 Practice Test - 7th grade

Consider the two statements:

Statement 1: If two line segments have the same length, then they are congruent.

Statement 2: If two line segments are congruent, then they have the same length.

A.

Statement 1 is true and statement 2 is false.

B.

Statement 1 is false and statement 2 is true.

C.

Both Statement 1 and statement 2 are true.

D.

Both Statement 1 and statement 2 are false.

#### SOLUTION

Solution : C

Two line segments are congruent only if they superimpose which is possible only if they have equal length and the converse is also true.
Hence, both the given statements are true.

If ΔABCΔRQP , then P = _____ .

A.

A

B.

C

C.

B

D.

Both A  and B

#### SOLUTION

Solution : B

If two triangles are congruent, then their corresponding angles are equal.

Here, Δ ABC  Δ RQP
A =R
B =Q
P =C
So, option B is correct.

The three sides of a triangle are equal to the corresponding three sides of another triangle, then the triangles are congruent by which condition?

A.

SAS

B.

SSS

C.

ASA

D.

RHS

#### SOLUTION

Solution : B

When three sides of a triangle are equal to corresponding three sides of another triangle, the triangles are congruent by Side-Side-Side (SSS) congruence.

In the above figure,
AB = PQ
AC = PR
BC = QR
Since the sides of ABC are equal to corresponding sides of PQR, ABCPQR by SSS criterion for congruency.

If two sides and the angle included between them in one of the triangles are equal to the corresponding sides and the angle included between them of the other triangle, then the triangles are congruent by ____.

A.

SAS congruence condition

B.

SSS congruence condition

C.

ASA congruence condition

D.

RHS congruence condition

#### SOLUTION

Solution : A

Two triangles are congruent if two sides and the angle included between them in one of the triangles are equal to the corresponding sides and the angle included between them of the other triangle. This condition is called SAS (Side, Angle included, Side) condition.

In the figure above,
AC = XZ
BC = YZ
ACB=YZX
ACBXZY by SAS criterion for congruency.

Two triangles are congruent if two angles and the side included between them in one of the triangles are equal to the corresponding angles and the side included between them, of the other triangle. This condition is

A.

SAS

B.

SSS

C.

ASA

D.

RHS

#### SOLUTION

Solution : C

Two triangles are congruent if two angles and the side included between them in one of the triangles are equal to the corresponding angles and the side included between them, of the other triangle. This condition is called ASA congruence criterion.

Two right-angled triangles are congruent if the hypotenuse and a leg of one of the triangles are equal to the hypotenuse and the corresponding leg of the other triangle. What is this condition called?

A.

SAS congruence condition

B.

SSS congruence condition

C.

ASA congruence condition

D.

RHS congruence condition

#### SOLUTION

Solution : D

Two right-angled triangles are congruent if the hypotenuse and the leg of one of the triangles are equal to the hypotenuse and the corresponding leg of the other triangle. This condition is called RHS congruence of two triangles and is applicable only to right angled triangles.

Consider the figure and choose the correct option.

A.

ΔABCΔDEF

B.

ΔABCΔDFE

C.

ΔABCΔFED

D.

ΔABC ΔFED

#### SOLUTION

Solution : C

In  ΔABC and ΔFED

BC = ED  (Given in the figure);
B =  E = 90
A =  F   (Given in the figure)

C = D  (Angle sum property of triangle)

Therefore, by ASA congruence condition, ΔABCΔFED .

Among two congruent angles, one has a measure of 60o, the measure of the other angle is ___(in degrees).

#### SOLUTION

Solution :

If two angles have the same measure, they are congruent. Also, if two angles are congruent, their measures are same.

Hence, the measure of the other angle is also 60o.

If two angles have the same measure, they are congruent.

A.

True

B.

False

#### SOLUTION

Solution : A

For two angles to be congruent, they should coincide when superimposed. This is only possible if both the angles are equal. Hence, the given statement is true.

If all the corresponding angles of two triangles are same, then the two triangles are necessarily congruent.

A.

True

B.

False

#### SOLUTION

Solution : B

If all the corresponding angles of two triangles are equal, then triangles will have the same shape, but not necessarily the same size and hence may not be congruent. See the figure below. The corresponding angles of both triangles are equal, but still their sizes are not same and hence they are not congruent.