Study Online and Download Notes of Mathematics 9th Unit 14: Ratio and Proportion. In this unit we will prove some theorems and corollaries involving ratio and proportions of sides of triangle and similarity of triangles.
Study Online and Download Notes of Mathematics 9th Unit 14: Ratio and Proportion. In this unit we will prove some theorems and corollaries involving ratio and proportions of sides of triangle and similarity of triangles. A knowledge of ratio and proportion is necessary requirement of many occupations like food service occupation, medications in health, preparing maps for land survey and construction works, profit to cost ratios etc.
Recall that we defined ratio a : b = a/b as the comparison of two alike quantities a and b, called the elements (terms) of a ratio. (Elements must be expressed in the same units). Equality of two ratios
was defined as proportion.
That is, if a : b = c : d, then a, b, c and d are said to be in proportion.'
After studying this unit, the students will be able to:
- prove that a line parallel to one side of a triangle, intersecting the other two sides, divides them proportionally.
- prove that if a line segment intersects the two sides of a triangle in the same ratio, then it is parallel to the third side.
- prove that the internal bisector of an angle of a triangle divides the side opposite to it in the ratio of the lengths of the sides
- containing the angle.
- prove that if two triangles are similar, the measures of their corresponding sides are proportional
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