Parallel lines and medians
Answers are for parents and teachers.
1
Parallel lines cut AB = BC on one transversal. On another, DE = 3x + 2 and EF = 5x − 6. Find x and DF.
3x + 2 = 5x − 6, so x = 4. DE = 14, DF = 28.
2
The sides of Δ ABC are 9, 12 and 15 cm. Find the three midsegments and the perimeter of the triangle they form.
4.5, 6 and 7.5 cm; perimeter 18 cm.
3
In a quadrilateral the diagonals are 12 cm and 20 cm. Find the perimeter of the quadrilateral formed by the midpoints of its sides.
Sides 6, 10, 6, 10: perimeter 32 cm.
4
The medians of a triangle meet at G and CF = 27 cm. Find CG and GF.
CG = 18 cm and GF = 9 cm.
5
A right-angled triangle has legs 5 cm and 12 cm. Find the median from the right angle.
Hypotenuse 13 cm, so the median is 6.5 cm.