Question

(practice test help!!) Teyla wants to find the distance, AB, across a river. She starts at point B, walks along the edge of the river for 94 feet, and marks point D. She turns 90°, walks until her final location, marks point E. Point E, point A, and point C are collinear. 1) Can Teyla conclude that ABC and EDC are similar?is so, what triangle similarity postulate/theorem can she use?2) Suppose DE = 103 ft. calculate the distance of AB to the nearest tenth of a foot. show your work. dont forget to label answer!

Answer 1

Consider the triangles ABC and EDC.

The angle ACB is equal to angle DCE, since they are vertically opposite angles.

Angle CDE is equal to the angle ABC, since both are right angles.

Consider that DE and AB are parallel line and EA is the transversal on it. Therefore, the angles DEC and BAC must also be equal, being alternate interior angles.

Since all the 3 cooresponding angles of the triangles are equal.

By using the AAA criteria, the triangles ABC and EDC are similar.

Hence , Teyla can also conclude that the triangles are similar, using AAA criteria.