SSS Congruence Criterion

Q. Given that $\square ACBD$ is a kite. By which congruence criterion are the triangles $ACB$ and $ADB$ congruent?

1. SAS
2. SSS
3. RHS
4. ASA

Q. If $△$PQR $\cong$ $△$XYZ by SSS criterion for congruency of triangles, then ____.

1. $\angle P=\angle Y$
2. $\angle P=\angle X,\angle Q=\angle Y,\angle R=\angle Z$
3. $\angle Q=\angle Z$
4. $\angle R=\angle X$

Q.

Prove that diagonals of a rectangle are equal in length.

Q.

In the given figure, if AB = CD and BC = DA, then which of the following is true?

1. $△ABC\cong △CDA$ by SSS postulate

2. $△ABC\cong △CDA$ by SSS postulate

3. AB // CD

4. BC // AD

Q. By which congruency criterion, the two triangles in the given figure are congruent?

Q. If two plane figures are congruent then they have

1. same shape and same size
2. same shape
3. same size
4. same angle

Q.

If the sides of $△ABC$ are AB = 5 cm, BC = 4 cm and CA = 3 cm, and sides of $△PQR$ are PQ = 4 cm, QR = 3 cm and RP = 5 cm, then _______.

1. $△ABC\cong △QPR$
2. $△ABC\cong △PQR$
3. $△ABC\cong △PRQ$
4. $△ABC\cong △RPQ$

Q.

Consider the figure below:

The two triangles are congruent by SAS criterion only.

1. False

2. True

Q. By which congruency criterion, the two triangles in the given figure are congruent?

1. SAS
2. RHS
3. SSS
4. ASA

Q. In the given figure, O is the centre of the circle. OD is a line bisecting AB at C. Which of the following statements are true?

1. $△$AOC is congruent to $△$BOC
2. $△$AOC is not congruent to $△$BOC
3. OA = OD = OB
4. OC = OB = OA

Q. ABCD is a square. $△ACD$ is congruent to $△ACB$ by _________

1. ASA criteria
2. RHS criteria
3. SAS criteria
4. SSS criteria

Q. If AO = CO, OB = OD and BA = DC in the given figure
then, find the angle of $△AOB$ that will correspond to $\angle C$ of $△COD$ is :

1. $\angle$B
2. $\angle$A
3. $\angle$D
4. $\angle$DOC

Q. Which of the following set is the correct set of corresponding angles for the figure given below?

1. $\angle PTQ=\angle RSQ$,
   $\angle TQP=\angle SQR$,
   $\angle QPT=\angle QRS$
2. $\angle PTQ=\angle RSQ$,
   $\angle TQP=\angle SRQ$,
   $\angle QPT=\angle QSR$
3. $\angle PTQ=\angle RSQ$,
   $\angle TQP=\angle QSR$,
   $\angle QPT=\angle SRQ$
4. None of the above

Q.

Using the information given in the figure, find the values of x and y.

1. $x=56°,y={76}^{\circ }$

2. $x={48}^{\circ },y={56}^{\circ }$

3. $x={48}^{\circ },y={76}^{\circ }$

4. $x={76}^{\circ },y={56}^{\circ }$

Q.

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

1. SAS

2. RHS

3. SSS

4. ASA

Q. Given AB = 3 cm, AC = 5 cm and $\angle B={30}^{\circ }$, $\Delta$ABC cannot be uniquely constructed, with AC as base, why?

1. The vertex A coincides with the vertex C.
2. The vertex B cannot be uniquely located.
3. The other two angles are not given.
4. Two sides and included angle are given.