Question : ABC is a right angle triangle and $\angle ABC = 90^{\circ}$. BD is perpendicular on the side AC. What is the value of $(BD)^2$?

Option 1: $AD\times DC$

Option 2: $BC\times AB$

Option 3: $BC\times CD$

Option 4: $AD\times AC$

Question : ABCD is a quadrilateral in which BD and AC are diagonals. Then, which of the following is true:

Option 1: AB + BC + CD + DA < (AC + BD)

Option 2: AB + BC + CD + DA > (AC + BD)

Option 3: AB + BC + CD + DA = (AC + BD)

Option 4: AB + BC + CD + DA > 2(AC + BD)

Question : If ABC is an equilateral triangle and D is a point in BC such that AD is perpendicular to BC, then:

Option 1: AB : BD = 1 : 1

Option 2: AB : BD = 1 : 2

Option 3: AB : BD = 2 : 1

Option 4: AB : BD = 3 : 2

Question : ABC is an isosceles triangle having $\angle$ C = 90$^\circ$, if D is any point on AB, then AD² + BD² is equal to:

Option 1: CD²

Option 2: 2CD²

Option 3: 3CD²

Option 4: 4CD²

Question : x, y, and z are the sides of a triangle. If z is the largest side and x² + y² > z², then the triangle is a:

Option 1: Isosceles right angled triangle

Option 2: Acute angled triangle

Option 3: Obtuse angled triangle

Option 4: Right angled triangle