Given: M ≅ X
N ≅ Y
YO ≅ NZ
Prove: △MNO ≅ △XYZ

Δ MNO ≅ ΔXYZ ⇒ proved down

Step-by-step explanation:

Cases of congruency

SSS ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ  SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and including angle in the 2nd Δ  ASA ⇒ 2 angles and the side whose joining them in the 1st Δ ≅ 2 angles and the side whose joining them in the 2nd Δ  AAS ⇒ 2 angles and one side in the 1st Δ ≅ 2 angles and one side in the 2nd Δ  HL ⇒ hypotenuse and leg of the 1st right Δ ≅ hypotenuse and leg of the 2nd right Δ  

Let us solve the question using the 4th rule above

∵ YZ = YO + OZ

∵ NO = NZ + ZO

∵ OZ = ZO ⇒ from the figure

∵ YO ≅ NZ ⇒ given

∴ YZ ≅ NO

In Δs MNO and XYZ

∵ ∠M ≅ ∠X ⇒ given

∵ ∠N ≅ ∠Y ⇒ given

∵ NO ≅ YZ ⇒ proved

→ By using the AAS postulate of congruency.

∴ Δ MNO ≅ ΔXYZ  

X=y+4 is the answe

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