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
