] imath - Graad 11 Wiskunde oefeninge i.v.m. loodlyne in sirkels, Grade 11 Mathematics, more exercises re. lines perpendicular to a chord.
WISKUNDE
NOG OEFENINGE

Loodlyne op koorde.

MATHEMATICS
MORE EXERCISES

Perpendicular lines to a chord.

Vind, met redes, die waarde van x en y
in elke figuur:

Find, giving reasons, the value of x and y
in each diagram :

1.1 OM ⊥  AB; AB = 8 cm;  OA = 5 cm;
AM = x;  OM = y

1.2 ME ⊥ CD;  ME = 5 mm;  MC = 13 mm;
CE = x;  CD = y

.

1.3 OM ⊥ AB;  ON ⊥ CD;  AB = 18 cm;
OC = 15 cm;  OM = x;  MON = y

1.4 ∠T = 32°;  ∠M = 22°
∠P = x;  ∠R1 = y

.

ABCD is 'n parallelogram met BC verleng na
E en AC || DE.

Bewys, met redes, dat
2.1 ACED 'n parallelogram is.
2.2 BC = CE.

ABCD is a parallelogram with BC produced
to E and AC || DE.

Prove, giving reasons, that
2.1 ACED is a parallelogram.
2.2 BC = CE. PQRS is 'n parallelogram met A die middelpunt
van PT en B die middelpunt van TR.

Bewys, met redes, dat
3.1 AQBS 'n parallelogram is.
3.2 ∠A1 = ∠B2.

PQRS is a parallelogram with A the midpoint of
PT and B the midpoint of TR.

Prove, giving reasons, that
2.1 AQBS is a parallelogram.
2.2 ∠A1 = ∠B2. KLMN is 'n parallelogram met PL = NQ.

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

KLMN is a parallelogram with LP = NQ.

Prove, giving reasons, that
KPMQ is a parallelogram. ABCD is 'n parallelogram met BC verleng na E
sodat AB = DE.

Bewys, met redes, dat
∠E = ∠ DCE.

ABCD is a parallelogram with BC produced
to E so that AB = DE.

Prove, giving reasons, that
∠E = ∠ DCE. ABCD is 'n parallelogram met E en F
punte op AD en BC respektiewelik.

Bewys, met redes, dat
6.1 EM = MF
6.2 AFCE 'n parallelogram is.

ABCD is a parallelogram with E and F points

Prove, giving reasons, that
6.1 EM = MF
6.2 AFCE is a parallelogram. KLMN is 'n parallelogram met ∠L1 = ∠N1.

Bewys, met redes, dat
7.1  KP = QM
7.2  PLQN 'n parallelogram is.

KLMN is a parallelogram with ∠L1 = ∠N1

Prove, giving reasons, that
7.1  KP = QM
7.2  PLQN is a parallelogram. 