Question

Given: Line NM is parallel to line OQ, like NE is congruent to line OQ, Line NR is perpendicular to line MP, line OP is perpendicular to line MP
Prove: NR congruent to OP

Answer 1

Answer:

Step-by-step explanation:

From the picture attached,

In ΔNMR and ΔOQP,

NM║OQ, and MP is the transversal intersecting these lines at M and Q.

∠NMR ≅ ∠OQP [Given]

m∠NRM = m∠OPQ = 90° [Given]

ΔNMR ~ ΔOQP [By AA property of similarity]

Therefore, corresponding sides of the similar triangles will be proportional.

$\frac{NM}{OQ}=\frac{MR}{QP}=\frac{NR}{OP}$

Since, NM ≅ OQ [Given]

Therefore, NR ≅ OP