Question

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

Answer 1

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]

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

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

1 + $\frac{OP}{MO}$ = 1 + $\frac{TR}{MT}$

$\frac{OP}{MO}=\frac{TR}{MT}$

In ΔTSR,

∠1 ≅ ∠2 [Given]

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

Therefore, $\frac{OP}{MO}=\frac{SR}{MT}$

Or $\frac{MO}{OP}=\frac{MT}{SR}$

Hence proved.