wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

ABC is a triangle right angled at C. A line through the mid point M of the hypotenuse AB and parallel to BC intersects AC at D. Show that,
(i) D is the mid-point of AC.
(ii) MDAC
(iii) CM=MA=12AB


Open in App
Solution

(i) In BAC,
M is the mid-point of AB and MD || BC.
D is the mid-point of AC.
(Converse of mid-point theorem)
AD=CD

(ii) ACB=ADM (Corresponding angles)
Also, ACB=90°
ADM=90° and MDAC

(iii) Consider AMD and CMD
DM=DM(Common side)
ADM=CDM (Right angle)
AD=CD (D is the mid-point of side AC)
So, by SAS congruence criterion, AMDCMD
CM=MA=12AB

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Criteria for Congruency
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon