True statement about tessellations are [tex]1, 2 \ \& \ 4[/tex].
" Tessellation is defined as the occupied the flat surface by using regular geometric shape repeatedly without overlapping and gap between them."
Property of tessellation
In tessellation interior angle of regular polygon is a divisor of [tex]360\°[/tex].
According to the question,
Statement 1: A tessellation can be made entirely of congruent equilateral triangles.
Interior angle of equilateral triangles is [tex]60[/tex]° , which is a divisor of [tex]360\°[/tex].
All equilateral triangles are congruent.
Tessellation is possible.
Statement [tex]1[/tex] is true.
Statement 2: A tessellation can be made entirely of congruent regular hexagons.
Interior angle of regular hexagon is [tex]120[/tex]° , which is a divisor of [tex]360\°[/tex].
All regular hexagon are congruent.
Tessellation is possible.
Statement [tex]2[/tex] is true.
Statement 3: A tessellation can be made entirely of congruent regular pentagons
Interior angle of regular pentagon is [tex]108[/tex]° , which is not a divisor of [tex]360\°[/tex].
All regular pentagon are congruent.
Tessellation is not possible.
Statement [tex]3[/tex] is not true.
Statement 4: A tessellation can be made entirely of congruent squares.
Interior angle of congruent squares is [tex]90[/tex]° , which is a divisor of [tex]360\°[/tex].
All squares are congruent.
Tessellation is possible.
Statement [tex]4[/tex] is true.
Hence, true statement about tessellations are [tex]1, 2 \ \& \ 4[/tex].
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