Question

2. AD is a median, BL and CM are perpendiculars drawn from B and Crespectively o
produced to M. Prove that BL = CM
​

Answer 1

In ∆ABD and ∆ACD

AD=AD (both are common)

BD=DC (because median divides the line in two

equal parts)

angle ADB=angle ADC (each of 90°)

therefore ∆ABD =~ ∆ACD by SAS congruency

so the AB=AC and angle B= angle C ( by c.p.c.t)

Now, in ∆BLC and ∆CMB

BC=CB ( both are common)

angle B= angle C ( we have already proof it)

as we know. that AB= AC so on dividing by 2 on both sides we found that their half is also equal

AB/2=AC/2

BM=CL

so , ∆ BLC is congruent to ∆ CMB by SAS congruency

therefore BL=CM ( by c.p.c.t)

hence proof

hope it helps you