ABC is a right angled triangle right angled at A. AD is the altitude through A. E is a point on AC such that AE=CD and F is a point on AB such that AF=BD. Prove that BE=CF.

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In a right triangle ABC, right-angled at B, D is a point on hypotenuse such that $B D \sim A C$ . If $D P \sim A B$ and $D Q \sim B C$ then prove that

(a) $D Q^{2} = D P . Q C$

(b) $D P^{2} = D Q . A P$

Q. In a triangle ABC AD is perpendicular to BC such that AB squared is equal to BD into CD prove that ABC is a right triangle right angle at A

Q. ABC is a triangle, D is a point on AB such that AD =

\frac{1}{4}

AB and E is a point on AC such that AE =

\frac{1}{4}

AC. Prove that DE =

\frac{1}{4}

BC.

Q. In Fig.,

D

is a point on side

B C

△ A B C

such that

\frac{B D}{C D} = \frac{A B}{A C} .

Prove that

A D

is the bisector of

∠ B A C

△ A B C

is a right triangle right angled at

A

such that

A B = A C

and bisector of

∠ C

intersects the side

A B

D

. prove that

A C + A D = B C

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