Parallelogram Worksheet

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____________ :CLASS ____________ :DATE ____________ :TIME

I.C. Middle School

Parallelogram Worksheet

.ABCD is a parallelogram with AB = AC-I .N is the midpoint of [BC] and E is the symmetric of A with respect to N .]Prove that ABEC is a rhombus, then deduce that C is the midpoint of [ED)1 ?What is the nature of the triangle AED)2

and

yOˆ z

are two adjacent supplementary angles. B and C are the

xOˆ y

-II

feet of the perpendiculars drawn from a point A on [Oy) to the bisectors of .

xOˆ y

and

yOˆ z

respectively

.Prove that OABC is a rectangle)1 .)Prove that the line (BC) is parallel to (xy)2 ABCD is a rectangle with center O, and F the symmetric of A with respect to-III .]the midpoint M of [OB .Show that FBOC is a rhombus

ABC is a right triangle at A. The bisector of [Ax) of BAC cuts [BC] at M. The-IV perpendiculars drawn from M to [AB] and [AC] cut [AB] and [AC] at P and Q

.respectively .Prove that PAQM is a square

Given a square ABCD, I and J the midpoints of [AB] and [BC] respectively.-V .The straight lines (IJ) and (AD) intersect at E . Show that the triangle AEI is right isosceles)1 .Deduce that: AJ = EB)2 BD) cuts (IJ) at F. Show that FE=FD()3 .(Prove that: (DI) ⊥ (BE)4 (Deduce that: (DI)

(AJ

ABC is an isosceles triangle with main vertex A. [AM] is the median relative to-VI .[BC]; place D the symmetric of C with respect to B Construct (l) the perpendicular bisector of [BD] and let F be its point of .]intersection with [BD .)Let E be the point of intersection of (l) and [AB

.Prove that AMEF is a parallelogram

:ABCD is a parallelogram such that-VII .

AB = 2BC and ABˆ C = 60



.)Let S be the midpoint of [AB] and I the symmetric of S with respect to (BC

.Prove that the quadrilateral BICS is a rhombus)1 .]L is the midpoint of [DC)2 ?What is the nature of SBCL .Deduce the nature of the triangle SIL)3 .SL] cuts [SI] at K and [BC] cuts [SI] at T[)4 ?What is the nature of STCK

LDˆ R = 60

Given a parallelogram LORD such that LO = 2LD and-VIII 

.]Let U be the midpoint of [DR

.Draw the parallel from U to (LD). It cuts [LO] at E)a ?What is the nature of the quadrilateral DUEL .)Place A the symmetric of L with respect to (DU)b ?What is the nature of triangle LDU .Prove that the quadrilateral DAUL is a rhombus)c