1]

– If ABCD is an isosceles trapezoid, then

AD = BC and AB || DC

∆DBC = ∆ACD (angles of tge base of the isosceles trapezoid are equal: ∠D = ∠C, AD = BC, BD – common side)

→ AC ≅ BD – Q.E.D.

2]

•In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a quadrilateral whose four sides all have the same length.

– Diagonal AC is common to two triangles: ABC and ACD

AB = AD and BC = CD

∆ABC = ∆ADC (On three sides)

Congruent triangles have equal angles → ∠BAD = ∠BCD