Question

if PM is a bisector of angleP and PM is a ray on QR. ThenΔpqm and ΔPRM are congruent by which criterion
a) ASA
b) SSS
c) SAS
d) none of these ​

Answer 1

Answer:

SAS congruence property

Answer 2

SSS (Side-side-side)
All three corresponding sides are congruent.
Eg: Consider △ABC and △PQR
PQ
AB
​
=
QR
BC
​
=
PR
AC
​
−
2
1
​

or AB=PQ,BC=QR,AC=PR
All the sides of triangle ABC are equal to all sides of △PQR

2. SAS [Side-angle-side]
Two sides and the angle between them are equal
In △ABC and △PQR,
AB=PQ;BC=QR,∠BAC=∠QPR
∴△ABC≅△PQR [by SAS Criteria]

3. AAS [angle-angle-side]
Two angles and a non- included sides are congruent.
Eg:
Consider the △ABC and △DEF,
BC∣∣EF and ∠ABC≅∠DEF .....(i)
∠BCA=∠EFD [corresponding angles of parallel lines are congruent].....(ii)
AD=CF
AD+CD=CF+CD [addition property of equality]
AC=AD+CD [partition postulate]
DF=CF+CD [partition postulate]
AC=DF [substitution property]....(iii)
From (i), (ii) and (iii),
△ABC≅△DEF [AAS Criteria]

4. ASA [angle-side-angle]
Two angles and the side between them are congruent.
Eg:
E is the mid-point of NO
∠SNW=∠TOA
Now, bisect ∠SNE and OA bisect ∠TOE ....(i)
As E is the midpoint, NE=EO.....(ii)
∠SEN≅∠TEO [vertical angles are congruent].....(iii)
From (i), (ii) and (iii),
△SNE≅△TOE [by ASA criteria]

i) SSS (side-side-side) = Option A
ii)SAS (side-angle-side) = Option D
iii)AAS (angle-angle-side) = Option C
iv) ASA (angle-side-angle) ) = Option B
solution