Question

if D is the mid point of hypotenuse AC of a right angled triangle ABC . write the value of BD in term of AC​

Answer 1

Answer:

Let ∆ABC is a right triangle such that ∠B = 900 and D is mid point of AC

we produce BD to E such that BD = AC and EC.

Now is ∆ADB and ∆CDE we have AD = DC [Given]

BD = DE [By construction]

And, ∠ADB = ∠CDE [Vertically opposite angles]

∴ By SAS criterion of congruence we have ∆ADB ≅ ∆CDE ⇒ EC = AB and ∠CED = ∠ABD ....(i) [By cpctc] But ∠CED & ∠ABD are alternate interior angles ∴ CE ║ AB ⇒ ∠ABC + ∠ECB = 1800 [Consecutive interior angles] ⇒ 90 + ∠ECB = 1800 ⇒ ∠ECB = 900 Now, In ∆ABC & ∆ECB we have AB = EC [By (i)] BC = BC [Common] And, ∠ABC = ∠ECB = 900 ∴ BY SAS criterion of congruence ∆ABC ≅ ∆ECB ⇒ AC = EB [By cpctc] ⇒ 1/2 AC = 1/2 EB ⇒ BD = 1/2 AC

Step-by-step explanation:

pls mark me the brainliest

Answer 2

Answer:

angojvihcicutv ihcihvoh

Step-by-step explanation:

what is thlngcdcgbhnk