Isosceles Triangle ABC

Hello sologuitar

Quote:

Originally Posted by sologuitar

Given: Isosceles triangle ABC with segment AB congruent to segment AC, and line CD is perpendicular to AB.

Prove: Segment BC multiplied by segment BC is equal to two times Segment AB multiplied by Segment BD.

Using Pythagoras' Theorem on $\triangle ADC$ :

$DC^2=AC^2-AD^2$
$= AB^2 -AD^2$ , since $AC = AB$ (given)

$=(AB+AD)(AB-AD)$

$=(AB+AD)(BD)$ ... (1)

And using Pythagoras' Theorem on $\triangle BDC$ :

$BC^2 = BD^2+DC^2$
$= BD^2 + (AB+AD)(BD)$ , from (1)

$=BD(BD +AB+AD)$

$=BD(AB+AB)$

$=2BD.AB$

Grandad