Question

Can someone help me prove these two triangles are similar?

Answer 1

As proved below

Explanation:

Triangle ABC - A (2,1), B (6,3) C (8,1)

Triangle ADE - A (2,1), D (4,2), E (5,1)

Using distance formula,

`vec(AB) = sqrt((6-2)^2 + (3-1)^2) = sqrt20`

`vec(AC) = sqrt((8-2)^2 + (1-1)^2) = 6`

`vec(AD) = sqrt((4-2)^2 + (2-1)^2) = sqrt5`

`vec(AE) = sqrt((5-2)^2 + (1-1)^2) = 3`

`(AB) / (AD) = sqrt20 / sqrt5 = sqrt(4*5)/sqrt5 = (2 cancelsqrt5)/sqrt5 = 2`

`(AC) / (AE) = 6/3 = 2`

`(AB) / (AD) = (AC) / (AE) = 2` and `hatA` is common in both the triangles.

Hence `Delta ABC, Delta ADE` are similar.

This can be confirmed by showing `(BC) / (DE)` also `= 2`