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Write a formal proof
Will give brainliest
Please answer with the full proofs

Write A Formal Proof Will Give Brainliest Please Answer With The Full Proofs class=

Sagot :

Answer:

Step-by-step explanation:

In ΔMOT and ΔMPR,

OT║PR and MR is a transverse,

Therefore, ∠MTO ≅ ∠MRP [Corresponding angles]

Similarly, OT║PR and MP is a transverse,

Therefore, ∠MOT ≅ ∠MPR [Corresponding angles]

ΔMOT ~ ΔMPR → [By AA postulate of similarity]

[tex]\frac{MP}{MO}= \frac{MR}{MT}[/tex] [Reason → Corresponding sides of the similar triangles are proportional]

[tex]\frac{MO+OP}{MO}=\frac{MT+TR}{MT}[/tex] [By segment addition postulate]

1 + [tex]\frac{OP}{MO}[/tex] = 1 + [tex]\frac{TR}{MT}[/tex]

[tex]\frac{OP}{MO}=\frac{TR}{MT}[/tex]

In ΔTSR,

∠1 ≅ ∠2 [Given]

Therefore, TR ≅ SR [Sides opposite to the equal angles in a triangle are equal]

Therefore, [tex]\frac{OP}{MO}=\frac{SR}{MT}[/tex]

Or [tex]\frac{MO}{OP}=\frac{MT}{SR}[/tex]

Hence proved.

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