Question

Rihanna wants to find the distance, AB, across a river. She starts at point B and walks along the edge of the river 76 ft and marks point C. Then she walks 24 ft further and marks point D. She turns 91° and walks until her final location and marks point E. Point E, point A, and point C are collinear.

Rihanna says she created similar triangles. Which postulate/theorem did she use to conclude that ∆ABC and ∆EDC are similar? Explain why she was able to use it?

Answer 1

Explanation:

Rihanna used the Angle-Angle (AA) postulate to conclude that ∆ABC and ∆EDC are similar.

The AA postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. In this case, Rihanna noticed that ∠ABC and ∠EDC are both right angles since they are formed by a line perpendicular to the river, and ∠CAB and ∠CED are congruent angles formed by the river. Therefore, by the AA postulate, ∆ABC and ∆EDC are similar.

Rihanna was able to use the AA postulate because the two triangles have corresponding angles that are congruent. This means that the two triangles have the same shape, but possibly different sizes. Since the triangles are similar, the ratios of the corresponding side lengths are equal. This means that she can use proportions to find the length of AB, the distance across the river, by comparing the corresponding side lengths of the two triangles.

For example, if we let x be the length of AB, then we have:

AC/AB = DC/DE

Substituting in the given values, we get:

76/x = (76+24)/DE

Simplifying and solving for x, we get:

x = 76DE/100

So, if we can find the length DE, we can use this proportion to find the length of AB.

hope this helps