Question
Are the triangles similar, if so why? What would be the correct similarity statement if similar? The triangles _____ similar. The reason they are similar is _____ The similarity statement would be _____
G.
14
45
R
49
84
84
24
H
(Options to use for the first blank is aren't, are. Options for the second blank is AA, SSS, aren't similar, SAS. Options for the last blank is GHS~RQS, aren't similar, GHS~QRS, GHS~QSR)
G.
14
45
R
49
84
84
24
H
(Options to use for the first blank is aren't, are. Options for the second blank is AA, SSS, aren't similar, SAS. Options for the last blank is GHS~RQS, aren't similar, GHS~QRS, GHS~QSR)
Answers
Answered by
GPT-4o mini
To determine if the triangles G and R are similar, we can analyze their corresponding angles and sides.
Given the measures:
- Triangle G has angles of 14° and 45°, which determines its third angle can be found since the sum of angles in a triangle is 180°. Thus, the third angle is \( 180° - (14° + 45°) = 121° \).
- Triangle R has angles of 49° and 84°. Calculating the third angle similarly, we find it is \( 180° - (49° + 84°) = 47°\).
Since the angles do not match, we need to check the corresponding side lengths provided:
- For triangle G, suppose we denote the sides corresponding to its angles as a, b, and c.
- For triangle R, denote the corresponding sides as x, y, and z.
Assuming the sides provided correspond:
- For G, sides are given as: 14, 45, and (unknown third side based on angles).
- For triangle R, the sides are given as: 49, 84, and (unknown third side).
To establish similarity via SSS, we would confirm the ratios of the lengths of the sides are equal. However, based on angles alone, we can use AA similarity if two angles match (if it were only using angles).
Since we do not see direct matching of angles or consistently proportional sides, it appears they do not correspond to similarity criteria.
Thus we conclude:
- The triangles **aren't** similar.
- The reason they are similar is **aren't similar**.
- The similarity statement would be **aren't similar**.
So the final placement would yield:
- The triangles **aren't** similar.
- The reason they are similar is **aren't similar**.
- The similarity statement would be **aren't similar**.
Given the measures:
- Triangle G has angles of 14° and 45°, which determines its third angle can be found since the sum of angles in a triangle is 180°. Thus, the third angle is \( 180° - (14° + 45°) = 121° \).
- Triangle R has angles of 49° and 84°. Calculating the third angle similarly, we find it is \( 180° - (49° + 84°) = 47°\).
Since the angles do not match, we need to check the corresponding side lengths provided:
- For triangle G, suppose we denote the sides corresponding to its angles as a, b, and c.
- For triangle R, denote the corresponding sides as x, y, and z.
Assuming the sides provided correspond:
- For G, sides are given as: 14, 45, and (unknown third side based on angles).
- For triangle R, the sides are given as: 49, 84, and (unknown third side).
To establish similarity via SSS, we would confirm the ratios of the lengths of the sides are equal. However, based on angles alone, we can use AA similarity if two angles match (if it were only using angles).
Since we do not see direct matching of angles or consistently proportional sides, it appears they do not correspond to similarity criteria.
Thus we conclude:
- The triangles **aren't** similar.
- The reason they are similar is **aren't similar**.
- The similarity statement would be **aren't similar**.
So the final placement would yield:
- The triangles **aren't** similar.
- The reason they are similar is **aren't similar**.
- The similarity statement would be **aren't similar**.