1883

Prove the blue angles are congruent and the red angles are congruent.

1849

The green shapes are regular pentagons. Prove the radius of the red circle is double the radius of the blue circle.

1848

The red shape is a regular pentagon. The right triangles are congruent. Prove the ratio of the hypotenuse to the side of the pentagon is $1+\sqrt{5}$.

1608

Given a regular pentagon. Prove the red hexagon can tessellate the plane.

1585

Given a regular pentagon. Prove the sum of the red line segments equals the sum of the blue line segments.

1584

Given two squares and a regular pentagon. Prove the red points are collinear.

1560

Given two squares and a regular pentagon. Prove the red points are collinear.

1249

Given a regular pentagon. Prove $\dfrac{a^2}{b^2}+\dfrac{b^2}{a^2}=3$.

1122

A regular pentagon and rectangle share a side. Prove the red area equals the blue area.

1099

The blue point is the centroid of the blue triangle. The green point is the centroid of the green triangle. The yellow points are the centroids of the yellow triangles. Prove the red shape is a parallelogram whose area is $2/9$ the area of the pentagon.

1026

Prove the red line segment is the side length of an inscribed regular pentagon.

910

Prove the red points are concyclic.

878

Given a regular pentagon. Prove $a+b+c=p+q$.

753

Find the area of the pentagon.

693

Each triangle with two adjacent sides of the pentagon has area $2$. Prove the pentagon has area $5+\sqrt{5}$.

593

Given a regular pentagon. Prove $a:b=b:c=c:d=\phi$.

545

Prove the circles are tangent to sides of the regular pentagon.

489

Find $x$.

461

Prove the area of the pentagon is $1/2$.

392

Prove red line segment is the side of a regular pentagon inscribed in the blue circle.