Question

A tree is represented by segment T1 to T2. The length of the shadow of the 5-foot tree (T1 to S1) is 12 yards, the height of the stick (S1 to S2) is 0.8 yards, and the length of the shadow of the stick (S1 to G1) is 1.5 yards. How can you prove the triangles are similar?

A) By showing the angles at S1 are equal.
B) By showing the angles at S2 are equal.
C) By showing the angles at T1 and T2 are equal.
D) By showing the angles at G1 are equal.

Answer 1

To prove the triangles are similar, one can show that the angles at S1 are equal. This confirms the triangles are similar by the Angle-Angle similarity postulate, as the trees and sticks make right angles with the ground and the angle of the sunlight is the same for both, creating equal corresponding angles at S1.

Step-by-step explanation:

To prove that the triangles in the scenario are similar, one would typically look for corresponding angles that are equal. In this case, we can consider the corresponding angles of the tree and its shadow, and the stick and its shadow. If the angles at S1 are equal, then by the Angle-Angle (AA) similarity postulate, the triangles are similar because two of their angles are the same. Here's why:

• Trees and sticks are vertical and make right angles (90 degrees) with the ground.
• The angle of the incoming light (sun rays) is the same for both the tree and the stick, thus the corresponding angles where the shadows start are equal.

Therefore, by showing that the angles at point S1 are equal, we can prove that the triangles are similar due to AA similarity. answer option A) is the correct method to prove the triangles are similar.