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A line is drawn parallel to one side of a triangle and cuts the other two sides. What does it do to those two sides?
ADivides them into equal parts
BDivides them in equal ratio
CLeaves them exactly as long
DMakes them equal in length
Answer & Solution
Correct answer: B. Divides them in equal ratio
1. The parallel line creates a smaller triangle sitting inside the original one.
2. Corresponding angles are equal, so the two triangles have the same shape.
3. The proportion theorem states that the two cut sides are divided in the same proportion as each other.
4. Equal ratio is not the same as equal parts, since the line need not be a mid-line.
5. Only when it passes through the mid-points does it cut the sides into halves.
_Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 8: Euclidean geometry_