ASA Congruence Criterion

Q. $△$STR is an isosceles triangle where ST = TR.
$\angle$PSR = $\angle$QRS = 90${}^{\circ }$.

Which of these is correct?

1. $△$PTS $\cong$ $△$QTR
2. $△$PTS $≆$ $△$QTR
3. SP = QT
4. RQ = ST

Q. An equilateral triangle is divided into two parts along one of its angle bisector as shown.

Which of the following statement(s) is/are correct?

1. CD = BD
2. $\angle$ADB = 90°
3. $\angle$ADC = $\angle$ADB = 60°
4. None of the above.

Q.
Given above are two triangles $△$ABC and $△$DEF. Which of the following statements is correct?

1. $△$ABC $\cong △$DEF by SAS criteria
2. $△$ABC $\cong △$DEF by SSS criteria
3. $△$ABC $\cong △$DEF by RHS criteria
4. $△$ABC $\cong △$DEF by ASA criteria

Q.

If $∆PQR\cong ∆LMN$ and $LN=18cm$ then which side of $∆PQR$ is also $18cm$ ?

Q. In the given figure, QTSR is a parallelogram. PQR is a straight line and QU = UT. Which of the following statements are correct?

1. $△PQU\cong △STU$
2. $QU=US$
3. $PQ=QR$
4. $PU=US$

Q. DF is equal to QR and $\angle$Q equals $\angle$D. Which is the closest criterion for congruency of triangles to prove the given two triangles are congruent?

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

Q. Two triangles are formed on the same base and equal angles at the ends of the base. The triangles are congruent by _____ criterion.

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

Q.

In the figure given below, AD and BC are equal and perpendicular to the same line segment AB. CD cuts AB at O. Then the relation between OC and OD is _____ .

1. $OD$ = $\frac{1}{2}$ $OC$

2. OD = OC

3. OD > OC

4. OD < OC

Q.

Consider the figure and choose the correct option.

1. $\Delta ABC\cong \Delta DEF$

2. $\Delta ABC\cong \Delta FED$​

3. $\Delta ABC\cong \Delta DFE$

4. $\Delta ABC$ $≆$ $\Delta FED$​

Q.
What criteria can be used to prove the given triangles are congruent?

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

Q. Two congruent triangles, $△ABC$ and $△QRP$, have $\angle A$ = $\angle Q$ = 40${}^{\circ }$, $\angle R$ = 65${}^{\circ }$ and QR = AB, then $\angle B$ = ____ .

1. 50${}^{\circ }$
2. 65${}^{\circ }$
3. 75${}^{\circ }$
4. 80${}^{\circ }$