Problems(2)
5 congruent triangles inside convex 5gon (2023 Novosibirsk Oral Geo Oly 7.4)
Source:
9/4/2023
Inside the convex pentagon , a point was chosen, and it turned out that all five triangles , , , and are congrunet to each other. Prove that these triangles are isosceles or right-angled.
geometrycongruent trianglespentagoncongruence
isosceles trapezoid wanted (2023 Novosibirsk Oral Geo Oly 9.4)
Source:
9/4/2023
In a trapezoid, the length of one of the diagonals is equal to the sum of the lengths of the bases, and the angle between the diagonals is degrees. Prove that this trapezoid is isosceles.
geometrytrapezoidIsosceles Trapezoidisosceles