Answer:
9. 1:1:1
10. a) 10cm
b) 20cm
Explanation:
9. The keys here are midpoints and parallel lines (creating similar triangles).
Because N is the midpoint of AM and BP||MQ, NP is a midsegment that divides AQ into 2 equal segments.
The same goes for M being the midpoint of BC and BP||MQ, dividing PC into 2 equal segments.
Since the same segment is equal to 2 different segments, those segments are also equal. And all three are equal to each other.
10. Since C & D are midpoints of AG & BG, CD is a midsegment of ΔABG and is therefore 1/2 the length of AB.
Since CD||EF, and C is the midpoint of AG, that makes CD a midsegment of ΔAFG, making CD 1/2 the length of FG. And the same applies to ΔBEG, making CD 1/2 the length of EG.