I need help !! This packet is due tomorrow and I have no idea what I’m doing .

The proof would be as follows:

Given: angle M congruent to angle X; angle N congruent to angle Y; YO congruent to NZ.

1. YZ=YO+OZ; reason: segment addition postulate (YZ is made up of YO and OZ).

2. ON=NZ+OZ; reason: segment addition postulate (ON is made up of NZ and OZ).

3. YO=NZ; reason: given.

4. ON=YO+OZ; reason: substitution (since NZ is congruent to YO, we substitute YO for NZ).

5. ON=YZ; reason: substitution (since YZ=YO+OZ, we substitute YZ for YO+OZ).

6. MNO is congruent to XYZ; reason: AAS (we have 2 sides and a non-included angle in each triangle congruent, which is the angle-angle-side theorem).

chisnau chisnau · Answer 2 · 2019-05-03T15:41:33+02:00

Answer:

Given is :

∠M≅∠X

∠N≅∠Y

YO≅NZ

We have to prove that ΔMNO≅ΔXYZ

Using segment addition postulate we get YZ=YO+OZ and ON=NZ+OZ and YO=NZ is already given. Using substitution of YO for NZ; we get ON=YO+OZ

Now substituting YZ for YO+OZ we get ON=YZ and also YZ=YO+OZ.

Now applying AAS we get ΔMNO is congruent to ΔXYZ because of angle-angle-side theorem as we have already proved that two sides are congruent and a non-included angle in each triangle is congruent.