Question

In the given figure, PS and QR intersect at O and OP = OS, OQ = OR

(i) Which one of the following is a standard criterion of congruency of two triangles ?

(a) SSS (b) RHS (c) SAS (d) ASA

(ii) If triangles are congruent then PQ =

(a) OP (b) OR (c) RS (d) OS

(iii) Which statement is correct ?

(a) ∆ POQ ≅ ∆ROS (b) ∆ POQ ≅ ∆SOR (c) ∆ POQ ≅ ∆ORS (d) ∆ POQ ≅ ∆OSR

iv) ∠POQ = ∠ROS because it is

(a) linear pair (b) alternate angles (c) vertical opposite angle (d) exterior angle​

Answer 1

Step-by-step explanation:

(i) Which one of the following is a standard criterion of congruency of two triangles ?

Clearly, we can see that the Congruency can be done only if the criterion is ASA.

SSS is not possible as only one side is given same.

RHS not applicable as 90° is not present in any case.

SAS not applicable as 2 sides are not made congruent as per now.

(ii) If triangles are congruent then PQ =

The traingles are congruent by CPCT, so PQ = RS

Hence, c) part.

(iii) Which statement is correct ?

(a) ∆ POQ ≅ ∆ROS (b) ∆ POQ ≅ ∆SOR (c) ∆ POQ ≅ ∆ORS (d) ∆ POQ ≅ ∆OSR

(a) ∆ POQ ≅ ∆ROS is the right congruency.

iv) ∠POQ = ∠ROS because it is

c) vertically opposite angles

Vertically Opposite angles are same and are in opposite sides of each other. Hence the name.

Answer 2

Answer:

$\longmapsto$ In the given figure, PS and QR intersect at O and OP = OS, OQ = OR.

(i) Which one of the following is a standard criterion of congruency of two triangle ?

$\implies$ (d) ASA.

(ii) If triangles are congruent then PQ =

$\implies$ (c) RS. PQ = RS.

(iii) Which statement is correct ?

$\implies$ (a) ∆ POQ ≌ ∆ ROS

(iv) ∠POQ = ∠RPS because it is

$\implies$ (c) vertical opposite angles.

Extra Information :-

➲ Rules Of Congruency :

$\implies$ There are 4 types of rules of congruency are as follows :

● SSS (Side-Side-Side)

● SAS (Side-Angle-Side)

● ASA (Angle-Side-Angle)

● AAS (Angle-Angle-Side)