Score to pass: 70%
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Thales Theorem Unit Summary
1. Midpoint: It is the point halfway between the endpoints of a line segment. For example, if AX = XB then X is the midpoint of line AB.
2. Thales' theorem states that if a line is drawn parallel to one side of a triangle intersecting the other two sides, it divides the two sides in the same ratio. For instance, in triangle ABC
Thales Theorem states that; \(\frac{BX}{XA}=\frac{CY}{YA}\)
3. The converse of Thales theorem states that if a line intersects two sides of a triangle and is not parallel to the third side, then it does not divide the sides in the same ratio.
4. The midpoint theorem for trapezia it states that the line through the midpoint of two non-parallel sides of a trapezium is parallel to the base of the trapezium.
5. The midpoint theorem states that:
a) The straight line through the midpoints of two sides of the triangle is parallel to the third side of the triangle.
b) The length of the segment joining the midpoints of the sides of the triangle is half the length of the third side which are parallel to it.
6. A ratio is a way of comparing two or more quantities of the same kind. For example 1:2, 3:4 are ratios.
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