RHS Criteria for Congruency of Triangles

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

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

Q. In trianglePQR; $\angle$ P = $\angle$Q = $\angle$ R
Find all the three angles of the triangle.

Q. In the given figure, prove that: [4 MARKS]



(i) $\Delta XYZ\cong \Delta XPZ$

(ii) YZ = PZ

(iii) $\angle YXZ=\angle PXZ$

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. 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.

For the given figure complete the congruence statement:

$△BCA\cong$ $△$ ___________

Q. (a) In the given figure, prove that: BD = BC.



(b) $\text{In the given figure,}\Delta ABC\text{and}\Delta OBC\text{are both isosceles.}$
Prove that $\Delta AOC$ is congruent to $\Delta AOB$.

[4 MARKS]

Q. (a) In the given figure, prove that:



(i) PQ = RS

(ii) PS = QR


(b) Which congruence criterion will you use in the following?

(i) Given: ∠ MLN = ∠ FGH

∠ NML = ∠ GFH

ML = FG

So, ΔLMN ≅ ΔGFH

(ii) Given: EB = DB

AE = BC

∠ A = ∠ C = 90°

So, ΔABE ≅ ΔCDB
.
​​​​​​​[4 MARKS]

Q.

Question 39

In the given figure (Q .No. 37) which of the following is true?
(a) $\angle 1=\angle 5$
(b) $\angle 4=\angle 8$
(c) $\angle 5=\angle 8$
(d) $\angle 3=\angle 7$

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

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

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

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

Q. In the given figure, if AB = AC, then which of the following statement(s) is/are true?

1. $△$ABD $\cong △$ACD by RHS postulate
2. $△$ABD $\cong △$ACD by ASA postulate
3. BD = DC
4. If $\angle$ABD = 60${}^{\circ }$, then, $\angle$ACD = 30${}^{\circ }$

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

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

Q. AP bisects $\angle BAC$
If the above statement is true then mention answer as 1, else mention 0 if false

Q. Which criterion of congruency is shown in the figure below?

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

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

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

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

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

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

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

Q.

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

1. x = 15, y = 9

2. x = 9, y = 15

3. x = 14, y = 9

4. x = 15, y = 10

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

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

Q. In a triangle PQR, $\angle P={60}^{\circ }$ and $\angle Q=\angle R$, find $\angle R$.

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. In the given figure, if
$\angle B=\angle Y=90°$
XZ = AC and YZ = BC, then the triangles are congruent by RHS criterion.

1. False
2. True

Q. In the figure, the two triangles are congruent. The corresponding parts are marked. We can write $\Delta$RAT$\equiv ?$