Question

ABC IS AN ISOCeles triangle with AB=AC. P is point on BC such that PM is perpendicular to AB and Pn is perpendicular to AC. prove that BM×NP=CN×MP

Answer 1

here angle ABC is congruent to angle ACB.... isosceles triangle theorem... (1)

now,

angle PMB is congruent to angle PNC.....(2)...both measure 90°

from (2)&(1),

triangle BMP is similar to triangle PNC.....by AA rest of similar triangles.

now,

BM/CN= PM/PN....similar sides in proportion

Therefore, hence proved

BM×PN=CN×MP....cross multiplying