In the diagram,LMN=ONM=90 degree.P is the mid point of MN,MN=2ML and MN=NO,Prove that (a)the triangles MNL and NOP are congruent
angle LMN= angle ONM = 90 degree (given)
MN= NO(given)
RHS
LN=OP
MNL is congruent to NOP
In the triangles MNL and NOP. <LMN=ONM=90 (given) ,MN=NO, MN=2ML (given), MN÷2=ML,MP=ML,MP=PN (P is the midpoint of MN). Therefore, ML=PN and since there are two sides and an angle, triangle MNL=NOP(SAS).
Hie,
I have seen the answer.However can you show your working
Regards
Style.
To prove that triangles MNL and NOP are congruent, we need to show that they have equal corresponding sides and equal corresponding angles.
Given:
- LMN = ONM = 90 degrees (Right angle)
- P is the midpoint of MN
- MN = 2ML (Given)
- MN = NO (Given)
First, let's start by identifying the corresponding sides:
1. MN and NO:
We are given that MN = NO. Therefore, one pair of corresponding sides is equal.
2. LN and OP:
Since P is the midpoint of MN, we can say that LP = PN (as P divides MN into two equal halves). Additionally, we know that ML is half the length of MN, so LN = 2ML. Since 2ML = LN and PN = LP, we can conclude that LN = OP.
Now, let's examine the corresponding angles:
1. Angle NML and angle NPO:
Both angles are right angles and equal to 90 degrees. So, NML = NPO.
2. Angle LNM and angle ONP:
Both angles are equal to 90 degrees, as given. So, LNM = ONP.
Based on our analysis, we see that all corresponding sides and angles are equal. Therefore, using the Side-Angle-Side (SAS) congruence criterion, we can conclude that triangles MNL and NOP are congruent.