Respuesta :

Answer:

Δ SJX  ~  Δ LXP

ΔSJX ~ ΔLXP    ….{Angle-Angle Similarity Postulate}  

Step-by-step explanation:

Given:

∠XSJ ≅ ∠XLP = 73°

∠SXJ = 54°

∠LXP = 53°

To Prove:

ΔSJX ~ ΔLXP

Proof:

Triangle sum property:

In a Triangle sum of the measures of all the angles of a triangle is 180°.

In ΔLPX,

[tex]\angle L+\angle P+\angle X=180\\\angle P=180-73-53=54\\\angle P=54\°[/tex]

∴ ∠SXJ ≅ ∠LPX = 54°   ..........Transitive Property ..( 1 )

In Δ SJX and Δ LXP  

∠XSJ ≅ ∠XLP          …………..{ measure of each angle is 73° given }  

∠SXJ ≅ ∠LPX = 54° ……….....{From  ( 1 ) above}  

ΔSJX ~ ΔLXP      ….{Angle-Angle Similarity Postulate}  ..Proved

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