RHS Congruence Criterion

Q. In the given figure, If AB = AC, then
$△ABD\cong △ACD$ by ____ criteria.

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

Q.

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

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

2. $x=56°,y={76}^{\circ }$

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

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

Q.
The triangles, $△$ADC and $△$DBE has equal hypotenuse. Their perpendiculars CA and ED have same length.
Choose the correct statement(s).

1. $\angle$CAD = $\angle$BED
2. CA = ED
3. $\angle$ADC = $\angle$DBE
4. CA = DB

Q. Two right-angled triangles have equal hypotenuse and base. Then the triangles are congruent by _____ criterion.

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

Q. If, $△DCA\cong △BED$ by RHS criteria and $\angle$DBE = 30${}^{\circ }$, then, what is $\angle$CAD?

1. 30°
2. 45°
3. 60°
4. 90°

Q. In the given figure AB = DC and AD = 5 cm. Find BC.

1. 5 cm
2. 4 cm
3. 3 cm
4. 6 cm

Q. A square is divided into two parts by drawing one of its diagonal. What all congruency criteria can be used to prove the two triangles formed congruent?

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

Q. Which criterion for congruency of triangles makes $△$ABC and $△$ADC congruent?

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

Q.
$\angle$SQR=30${}^{\circ }$, $\angle$QRS=$\angle$PSR=90${}^{\circ }$ and PR=QS.
What is the measure of $\angle$SRP

1. 30${}^{\circ }$
2. 40${}^{\circ }$
3. 50${}^{\circ }$
4. 60${}^{\circ }$

Q.

In the given figure, if AB = BC and $\angle BAO=\angle BCO={90}^{\circ }$, then which of the following is true?

1. $△ABO\cong △CBO$ by RHS postulate
2. $△ABO\cong △CBO$ by ASA postulate
3. OA = OC
4. If $\angle ABO={60}^{\circ }$ then, $\angle CBO={60}^{\circ }.$

Q. In the figure given below, $\angle BCD={60}^{\circ }$.
What is the measure of $\angle$BDA?

1. 40${}^{\circ }$
2. 60${}^{\circ }$
3. 50${}^{\circ }$
4. 30${}^{\circ }$

Q. If $△$ACD is congruent to $△$BDC, then which side of $△$BDC corresponds to side AC?

1. CB
2. DC
3. BD
4. None of the above