Question

if PQ = DE , < R = < F , < PQR = < DEF , then the congruency rule is
(a) SSS (b) SAS (c) ASA (d) AAS​

Answer 1

Answer:

Option (d) is correct. AAS.

Step-by-step explanation :

If PQ = DE, <R = <F, <PQR = <DEF, then the congruency rule is AAS (Angle Angle Side) Because corresponding two angles are equal and corresponding one side is equal. And side is not included in both equal angles.

Why other options are incorrect :

(a) SSS (Side, Side, Side) :

• For this congruence rule we need all three corresponding sides of triangle be equal but we have one side equal. Hence this is incorrect option.

(b) SAS (Side, Angle, Side) :

• For this congruence rule we need two corresponding sides of triangle be equal and one angle equal which should be included in both corresponding sides but we have one side and two angles equal. Hence this is incorrect option.

(c) ASA (Angle Side Angle) :

• For this congruence rule we need one corresponding side of triangle be equal which should be included between two corresponding equal angles. And we have one side equal which is not included between two equal angles. Hence, This is incorrect option.

Answer 2

Answer:

The correct option is C

SAS rule

Two sides and included angle of the first triangle are equal to two sides and the included angle of the second triangle.

So the two triangles DEF and PQR are congruent by the SAS rule.