If a perpendicular is drawn from the right angle vertex of a right-angled triangle to the hypotenuse, then the two triangles formed on either side of that perpendicular are similar to each other. — Prove it.

Q.If a perpendicular is drawn from the right angle vertex of a right-angled triangle to the hypotenuse, then the two triangles formed on either side of that perpendicular are similar to each other. — Prove it.

Given: ABC is a right-angled triangle with ∠A as the right angle, and a perpendicular AD is drawn from the right angle vertex A to the hypotenuse BC. To prove: Triangles ∆DBA and ∆DAC are similar. Proof: In ∆DBA and ∆ABC, ∠BDA = ∠BAC = 90° And ∠ABD = ∠CBA Therefore, the remaining ∠BAD = ∠BCA So, ∆DBA and ∆ABC are equiangular Therefore, ∆DBA is similar to ∆ABC Again, in ∆DAC and ∆ABC, ∠ADC = ∠BAC = 90° ∠ACD = ∠BCA Therefore, the remaining ∠CAD = ∠CBA So, ∆DAC and ∆ABC are equiangular Therefore, ∆DAC is similar to ∆ABC Now, since ∆DBA is similar to ∆ABC and ∆DAC is similar to ∆ABC Therefore, ∆DBA is similar to ∆DAC (Proved)

Left Side	Right Side
(a) A parallelogram inscribed in a circle	(i) Proportional
(b) If two circles touch internally, the distance between their centers is —	(ii) Right angle
(c) The corresponding sides of two similar-angled triangles are	(iii) Rectangle
(d) An angle in a semicircle	(iv) Difference in radii