Proportions in Triangles

the angles which occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

 If a line divides two sides of a triangle proportionally, then it is parallel to the third side

is a number which scales, or multiplies, some quantity. In the equation y = Cx, C is the scale factor for x. C is also the coefficient of x, and may be called the constant of proportionality of y to x.

are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal. In this example, these are two pairs of Alternate Interior Angles: c and f.

 look at that outside space for each crossed line, on different sides of the transversal. We hope you said ∠1 , ∠2 , ∠7 , and ∠8 are the exterior angles. We also hope you identified ∠1 and ∠8 as a pair of alternate exterior angles and ∠2 with ∠7 as the other pair.

is equal to the sum of the two opposite interior angles.

If the measures of the corresponding sides of two triangles are proportional then the triangles are similar. Likewise if the measures of two sides in one triangle are proportional to the corresponding sides in another triangle and the including angles are congruent then the triangles are similar.