Question

1)
The perpendicular from the square corner of
a right triangle cuts the opposite side into two
parts of 2 and 3 centimetres length.
2 em
3 em
i)
Prove that the two small right triangles cut by the perpendicular
have the same angles.​

Answer 1

The perpendicular from the square corner of a right triangle cuts the opposite side such that two small right triangles  have the Same Angles

Step-by-step explanation:

Let say Right angle Triangle ΔABC  right angled at B

∠B = 90°

∠A = x

∠C = y

∠A + ∠B + ∠C = 180°

=> 90° + x + y = 180°

=> x + y = 90°

=> x = 90° - y  or y = 90° - x

Let say BD ⊥ AC  cut AC into 2 cm & 3 cm length

in Δ ABD

∠ADB = 90°  BD ⊥ AC

∠A = x

∠ABD = 180° - 90° - x

=> ∠ABD =  90° - x

=> ∠ABD = y

in Δ CBD

∠CDB = 90°  as BD ⊥ AC

∠C = y

∠CBD = 180° - 90° - y

=> ∠CBD =  90° - y

=> ∠CBD = x

Now in Δ ABD & Δ CBD

∠ADB = ∠CDB = 90°

∠A = ∠CBD = x

∠ABD = ∠C = y

Hence Proved Both the triangles have the Same Angles