# Geometry Problem 1504: Squares, Equilateral Triangle, Parallel, Angle. Difficulty Level: High School

In the given figure, ABCD, EFGC, and EBHI are squares, and AED is an equilateral triangle. The task is to find the measure of angle GJH.

## Definitions and Suggestions

• A square is a two-dimensional geometric shape that has four equal sides and four right angles..
• An equilateral triangle is a type of triangle in which all three sides have equal length. It is a regular polygon with three sides, and it has three equal interior angles, each measuring 60 degrees.
• Parallel lines are two lines in a plane that never meet or intersect, no matter how far they are extended.
• An angle is a figure formed by two rays, or half-lines, that have a common endpoint and extend in different directions.
• Suggestion: Angles having their sides parallel, each to each, an extending in the same direction, or in opposite directions, from the vertices, are equal.

### Poem: Square, Equilateral Triangle

In the world of shapes, so bright and fair,
We find the square, a form so rare.
Four equal sides and angles right,
A shape so perfect, it shines with light.

Two triangles, equilateral in kind,
Their beauty shines, with every line.
Each side the same, so clear to see,
Symmetry they bring, for you and me.

Parallel lines that stretch so far,
Their distance constant, like a star.
They never meet, no matter where,
Their angles match, with such great care.

Angles and lines, so pure and true,
A mathematician's dream come true.
Symmetry and order, every day,
In shapes that dazzle, come what may.

In these forms, we see the power,
Of mathematics, hour by hour.
Angles, sides, and symmetry,
A poetic form of harmony.

So let us marvel at their grace,
These shapes that mathematics trace.
Square, triangles, lines that shine,
A world of beauty, so divine.