If a right circular cone is intersected by a plane only at its vertex, as in the picture below, what shape is produced?​

A right circular cone can be intersected by some plane to produce circle, ellipse, hyperbola depending upon where the plane is crossing the cone.

But if the plane crosses at the vertex. Just one point is crossed.

so, converting firstly the mixed fractions to improper fractions and then "adding".

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)