The Mathematics 11 Solving Problems with （11的数学解决问题）.pdf

The Mathematics 11 Competency Test Solving Problems with Similar Triangles In the previous document in this series, we defined the concept of similar triangles, ∆ABC ∼∆A’B’C’ as a pair of triangles whose sides and angles could be put into correspondence in such a way that it is true that property (i): A = A’ and B = B’ and C = C’. a b c property (ii): a b c If property (i) is true, property (ii) is guaranteed to be true. If property (ii) is true, then property (i) is guaranteed to be true. We also demonstrated some strategies for establishing that two triangles are similar using property (i). This is very useful to be able to do, since then, we may be able to use the property (ii) conditions to calculate unknown lengths in the triangles. Example 1: Given that lines DE and AB are parallel B in the figure to the right, determine the value of x, the distance between points A and D. E 11 solution: 7 First, we can demonstrate that A x D ∆CDE ∼∆CAB 15 C because C = C (by identity) and ∠CDE = ∠CAB because line AC acts as a transversal across the parallel lines AB and DE, and since ∠CDE and ∠CAB are corresponding angles in this case, they are equal. Since two pairs of corre