in the adjoining figure , pa is perpendicular to ab , qb perpendicular to ab and pa = qb - Maths -

Question

in the adjoining figure , pa is perpendicular to ab , qb
perpendicular to ab and pa = qb if pq intersect ab at o , show that
o is the midpoint of ab as well as that of pq

Utsav · Accepted Answer

Here the figure is missing but the solution is being provided based
on the following figure

<img alt="" src=
"https://img-nm%20mnimgs%20com/img/study_content/content_ck_images/images/HRHTR%20png"
style="width: 267px; height: 260px;">
In ∆AOP and ∆BOQ,we have∠AOP = ∠BOQ (vertically
opposite angles)∠OAP=∠OBQ(as PA and QB are perpendicular to
AB)AP = BQ(given)Hence by AAS congruency ,∆AOP ≅
∆BOQ∴By cpct AO =BO and OP=OQ Hence we can say that O
is the midpoint of both AB and PQ

in the adjoining figure , pa is perpendicular to ab , qb perpendicular to ab and pa = qb . if pq intersect ab at o , show that o is the midpoint of ab as well as that of pq