Question

Plot A(0, 0), B(1, 0), C(1, 2), D(2, 0), and E(2, 4). Then sketch ∆ABC and ∆ADE. By what postulate or theorem could you show that ∆ABC and ∆ADE are similar? A. AA Similarity Postulate B. SAS Similarity Theorem C. SSS Similarity Theorem D. Any of the above could be used to show that the triangles are similar.

Answer 1

1) Please find attached the given plot and sketch of the points created with Microsoft Word

2) The correct option is;

A. AA Similarity Postulate

Explanation:

1) Please find attached the given plot and sketch of the points created with Microsoft Word

2) The given parameters are;

The coordinates of the points are A(0, 0), B(1, 0), C(1, 2), D(2, 0) and E(2, 4)

Therefore, we have;

The length of segment AB = 1

The length of segment BC = 2

The length of segment AD = 2

The length of segment DE = 4

Therefore, we have;

∠ABC = ∠ADE = 90°

∠BAC = = artctan(2/1) = ∠DAE = artctan(4/2) = 63.435°

Therefore, ΔABC and ΔADE are similar by AA Similarity Postulate