] imath - Graad 10 Wiskunde oefeninge i.v.m. ewewydige lyne wat ander twee syse verdeel in driehoeke, Grade 10 Mathematics, more exercises re. parallel lines in a triangle.
WISKUNDE
NOG OEFENINGE

Driehoeke en ewewydige lyne.

MATHEMATICS
MORE EXERCISES

Triangles and parallel lines.

In meegaande skets is AD = DC en DE
halveer BC.

Gebruik die figuur en bewys, met redes, dat
FG = GC

In the accompanying diagram AD = DC and
DE bisects BC.

Use the diagram to prove, giving reasons, that
FG = GC In meegaande skets is AB || CD || EF
en C is die middelpunt van AE.

Bewys, met redes, dat
2.1 BG = EG
2.2 BD = DF
2.3 CD = ½(AB + EF)

In the accompanying diagram AB || CD || EF
and C is the midpoint of AE.

Prove, giving reasons, that
2.1 BG = EG
2.2 BD = DF
2.3 CD = ½(AB + EF) In meegaande skets is PS || TU || QR
en PT = TQ. Hoeklyne PR en QS sny TU in
A en B onderskeidelik.

Bewys, met redes, dat
3.1 TA = BU
3.2 AB = ½(PS − QR)

In the accompanying diagram PS || TU || QR
and PT = TQ. Diagonals PR and QS
intersect TU in A and B respectively.

Prove, giving reasons, that
3.1 TA = BU
3.2 AB = ½(PS − QR) In meegaande skets is K, L, M en N die
middelpunte van AB, BC, CD en DA
onderskeidelik. BD is 'n hoeklyn.

Bewys, met redes, dat
4.1 KN || LM
4.2 KLMN is 'n parallelogram.
4.3 KL + LM + MN + NK  =  AC + BD

In the accompanying diagram K, L, M and N
are the midpoints of AB, BC, CD and DA
respectively. BD is a diagonal.

Prove, giving reasons, that
4.1 KN || LM
4.2 KLMN is a parallelogram.
4.3 KL + LM + MN + NK  =  AC + BD In meegaande skets is K, L en M die
middelpunte van DE, DF en EF
onderskeidelik. KM en LM is verbind.

Bewys, met redes, dat ∠K1 = ∠L1

In the accompanying diagram K, L and M
are the midpoints of DE, DF and EF
respectively. Lines KM and LM are drawn.

Prove, giving reasons, that ∠K1 = ∠L1 In meegaande skets is AM = MB en
MP || BC. BP word verleng na Q sodat
BP = PQ. Q word verbind met A en C.

Bewys, met redes, dat ABCQ 'n
parallelogram is.

In the accompanying diagram AM = MB and
MP || BC. BP is produced to Q so that
BP = PQ. Q is joined to A and C.

Prove, giving reasons, that ABCQ is
a parallelogram. In Δ DEF is K die middelpunt van EF,
L die middelpunt van DK en EM || KN.

Bewys, met redes, dat DF = 3 DM.

In Δ DEF K is the midpoint of EF,
L is the midpoint of DK and EM || KN.

Prove, giving reasons, that DF = 3 DM. 