Question

3. According to the information given, what can you determine about the trianglesformed by Tyler, the mirror, and the peak? How do you know the relationship betweenthe two triangles? (4 points: 2 points for correctly describing the triangles, 2 points forthe explanation)4. To find the height of the peak, list the corresponding sides and angles of the twotriangles you and Tyler have created. (6 points: 1 point for each pair of sides orangles)

Answer 1

3. When Tyler sees the peak in the mirror, angle of incidence " i " and angle of reflection " r " made by incident ray AE and reflected ray CE will be equal.

Now we can easily say ∠ r = ∠ C ( Alternate angles )

∠ i = ∠ A ( alternate angles)

Since ∠ i = ∠ r

Therefore, ∠ A = ∠ C

∠B = ∠D = 90°

and ∠ACB = ∠ECD

Hence ΔABC is similar to ΔEDC.

4. Corresponding sides of these similar triangles are AB and CD, BE and ED, AE and EC.