1. Given
2. ∠LMO = 90° and ∠LMO = 90°
3. ∠LMO ≅ ∠LMO
4. Reflexive property of congruence
5. AA similarity theorem
Solution:
To prove: [tex]\Delta \mathrm{LMO} \sim \Delta \mathrm{PNO}[/tex]
Step 1: Given
[tex]\underline{L M} \perp \underline{M O}, \ \ \ \underline{PN} \perp \underline{M O}[/tex]
Step 2: Definition of ⊥ (perpendicular),
Two lines are perpendicular if and only if they form 90°.
∠LMO = 90° and ∠LMO = 90°
Step 3: All right angles are ≅ (congruent).
∠LMO ≅ ∠LMO
Step 4: Reflexive property of congruence.
Any angle is reflexive to itself.
∠O ≅ ∠O
Step 5: By AA similarity theorem,
ΔLMO and ΔPNO are similar.
ΔLMO [tex]\sim[/tex] ΔPNO
Hence proved.
