Question

1. in each pair, some of the angles of two triangles in degrees are given. use the information to decide if the triangles are similar or not. explain how you know.

s. triangle a: 53, 71, 124; triangle b: 53, 71, 124
s. triangle c: 90, 37, _; triangle d: 90, 53, _
ns. triangle e: 63, 45, _; triangle f: 14, 71, _
ns. triangle g: 121, _, _; triangle h: 70, _, _

Explanation:

Step1: Recall angle - sum property

The sum of interior angles of a triangle is 180 degrees. Also, two triangles are similar if their corresponding angles are equal.

Step2: Analyze Triangle A and B

For Triangle A with angles 53, 71, 56 (since 180-(53 + 71)=56) and Triangle B with angles 53, 71, 56. Since all corresponding angles are equal, they are similar.

Step3: Analyze Triangle C and D

In Triangle C, the third - angle is 180-(90 + 37)=53. In Triangle D, the third - angle is 180-(90 + 53)=37. Since the corresponding angles are equal (90 = 90, 37 = 37, 53 = 53), they are similar.

Step4: Analyze Triangle E and F

In Triangle E, the third - angle is 180-(63 + 45)=72. In Triangle F, the third - angle is 180-(14 + 71)=95. Since the corresponding angles are not equal, they are not similar.

Step5: Analyze Triangle G and H

Since the given angles 121 and 70 are not equal, and without further information about the other angles, we can already say they are not similar as one pair of angles is not equal.

Answer:

• Triangle A and B are similar because all corresponding angles are equal.
• Triangle C and D are similar because all corresponding angles are equal.
• Triangle E and F are not similar because corresponding angles are not equal.
• Triangle G and H are not similar because at least one pair of given angles is not equal.