If D is the midpoint of the hypotenuse AC of a right-angled AABC,
prove that BD = half of ac.
Answers
Answer:
If D is the mid point of the hypotenuse AC of a right angle triangle ABC, prove that BD is equal to 1/2 AC?
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7 Answers

Ravi Shankar, Ph.D. Electrical Engineering & Mathematics, Indian Institute of Science, Bangalore (1993)
Updated May 17, 2018 · Author has 331 answers and 491.7Kanswer views

Given:
Right angle triangle ΔABCΔABC where ∡ABC=90∘∡ABC=90∘
BDBD divides ACAC, i.e., AD=DCAD=DC
From DD, draw EDED and FD⊥FD⊥ to ABAB and BCBCrespectively
In DEBFDEBF, Because ∡BED = ∡BFD = ∡FBE = 90∘, ∠EDF=90∘∡BED = ∡BFD = ∡FBE = 90∘, ∠EDF=90∘. Therefore, DEBFDEBF is a rectangle. Hence, BE = DF, ED = BFBE = DF, ED = BF.
In Δs AEDΔs AED and DFCDFC,
∡EAD = ∡FDC
Answer:
BD=½AC
Step-by-step explanation:
If D is the mid point of AC, the line BD creates two triangles i.e, ABD and CBD
So acc to SAS property, BD=BD, AD=CD, and angle ABD= angle CBD
Hence proved