Two rectangles share a vertex. Two line segments connecting opposing vertices and the common side intersect in a single point. Prove that the rectangles are similar.

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## Solution

## Visual solution

## Poem

The miniature version

I’m smaller

Than this one much bigger

I’m a square in miniature

As important for the future

Than the blue one here

Nearly my brother

He is my lover

The blue square is larger

But I’m red and much stronger

For you our users

We are both believers

## One reply on “The miniature version”

With reference to your solution diagram,

Triangles DHA and GHF are similar, giving,

HA/HF = b/d…..(1).

Triangles AHB and FHE are similar giving,

AH/FH = a/c….(2)

From (1) and (2)

b/d = a/c or a/b = c/d.