Why SSA and AAA Congruency Rule Is Not Valid

Q. Question 2 (ii)
ABCD is a quadrilateral in which $AD=BCand\angle DAB=\angle CBA$ (See the given figure). Prove that
BD = AC

Q. Question 1
In $\Delta ABC$ and $\Delta PQR$, $\angle A=\angle Q$ and $\angle B=\angle R$. which side of a $\Delta PQR$ should be equal to side AB of $\Delta ABC$, so that the two triangles are congruent? Give reason for your answer.

Q. Which of the following options is/are appropriate criteria for congruence?

1. S.S.S.
2. A.A.A.
3. A.S.A.
4. S.A.S.

Q.

If $\Delta ABC$ $\cong$ $\Delta DEF$ by S.S.S. congruence, then which of the following options is correct?

1. AB = EF, BC = FD, CA = DE

2. AB = FD, BC = DE, CA = FE

3. AB = DE, BC = EF, CA = FD

4. AB = DE, BC = FD, $\angle$C = $\angle$F

Q.

If these triangles are congruent, then choose the property by which they are congruent.

1. ASA

2. SSS

3. SAS

4. These triangles can't be proven to be congruent

Q. If two sides and one angle of a triangle are equal to the two sides and angle of another triangle, then the two triangles are congruent.

1. True
2. False

Q.

If $\Delta ABC$ $\cong$ $\Delta DEF$ by S.S.S. congruence, then which of the following options is correct?

1. AB = EF, BC = FD, CA = DE

2. AB = FD, BC = DE, CA = FE

3. AB = DE, BC = EF, CA = FD

4. AB = DE, BC = FD, $\angle$C = $\angle$F

Q. If $\Delta ABC$ $\cong$ $\Delta DEF$ by SSS congruence, then, match the corresponding equal sides.

1. DE
2. EF
3. FD

Q.

If three sides of one triangle are equal to the three sides of another triangle, then, the two triangles are congruent by __ congruence condition.

Q.

If $\Delta ABC$ $\cong$ $\Delta DEF$ by S.S.S. congruence, then which of the following options is correct?

1. AB = DE, BC = EF, CA = FD

2. AB = EF, BC = FD, CA = DE

3. AB = FD, BC = DE, CA = FE

4. AB = DE, BC = FD, $\angle$C = $\angle$F

Q.

If three angles of a triangle are equal to three angles of another triangle respectively, then the two triangles are congruent.

1. True

2. False