Two triangles `DeltaABC and Delta DEF` are given such that `AB"||"DE,BC"||"EFandAB=DE,BC=EF.`"Show that"AC"||"DFandAC=DE`

In figure, AB||DE, AB=DE, AC||DF and AC=DF. Prove that BC||EF and BC=EF.

In Figure DE||BC and CD||EF. Prove that A D^2=A B*A F .

Which of the following pairs of triangles are congruent ? In each case, state the condition of congruency : (a) In Delta ABC and Delta DEF , AB = DE, BC = EF and angle B = angle E . (b) In Delta ABC and Delta DEF, angle B = angle E = 90^(@) , AC = DF and BC = EF. (c) In Delta ABC and Delta QRP , AB = QR, angle B = angle R and angle C = angle P . (d) In Delta ABC and Delta PQR , AB = PQ, AC = PR and BC = QR. (e) In Delta ABC and Delta PQR , BC = QR, angle A = 90^(@), angle C = angle R = 40^(@) and angle Q = 50^(@) .

The following figure shows a triangle ABC in which AD and BE are perpendiculars to BC and AC respectively. Show that : CD xx AB = CA xx DE

In DeltaABC and DeltaDEF , angleB=angleE,angleF=angleC and AB=3DE. Then, the two triangles are

The following figure shows a triangle ABC in which AD and BE are perpendiculars to BC and AC respectively. Show that : DeltaABC ~ DeltaDEC

In triangle ABC, D is a point in side AB such that AB = 4AD and E is a point in AC such that AC = 4AE. Show that BC : DE = 4:1

In a hexagon ABCDEF circumscribe a circle, prove that AB+CD+EF=BC+DE+FA.

ABC is a triangle in which AB = AC and D is a point on AC such that BC^2 = AC xx CD .Prove that BD = BC .

In figure , BA _|_ AC,DE _|_DF such that BA = DE and BF = EC . Show that Delta ABC cong Delta DEF.