Application of Pythagoras Theorem

From given figure, In ∆ABC, AB ⊥ BC, AB = BC then m∠A = ?

In the given figure, ∠B < 90° and segment AD ⊥ BC, show that

(i) b² = h² + a² + x² – 2ax

(ii) b² = a² + c² – 2ax

In an isosceles triangle ABC, if AB = AC = 13 cm and the altitude from A on BC is 5 cm, find BC.

From given figure, In ∆ABC, AB ⊥ BC, AB = BC, AC = `2sqrt(2)` then `l` (AB) = ?

If the sides of a triangle are 3 cm, 4 cm, and 6 cm long, determine whether the triangle is a right-angled triangle.

Construct a triangle ABC with sides BC = 7 cm, ∠B = 45° and ∠A = 105°. Then construct a triangle whose sides are `3/4` times the corresponding sides of ∆ABC.

In a right ∆ABC right-angled at C, if D is the mid-point of BC, prove that BC² = 4(AD² − AC²).