Mikel is determining if the two triangles below could be similar based on their side lengths.
Triangle R S T. Side R S is 3 centimeters, side S T is 6 centimeters, and side R T is 8 centimeters. Triangle W X U. Side W X is 18 centimeters, side X U is 7.5 centimeters, and side W U is 15 centimeters.
Which statements accurately describe the triangles? Check all that apply.
The common ratio between the triangles is 3 because StartFraction 18 Over 6 EndFraction = 3.
The common ratio between the triangles is 2.5 because StartFraction 7.5 Over 3 EndFraction = 2.5.
The triangles could be similar.
The triangles could not be similar.
The ratios of the side lengths are not consistent.
The ratios of the side lengths are consistent.
The triangles could be similar. The ratios of the side lengths are consistent.
The triangles below are similar.
Triangle A B C. Side A C is 10 and side A B is 5. Angle C is 30 degrees. Triangle D E F. Side E D is 7.5 and side D F is 25. Angle F is 30 degrees and angle E is 90 degrees.
Which similarity statements describe the relationship between the two triangles? Check all that apply.
Triangle C B A is similar to triangle F E D
Triangle C B A is similar to triangle F D E
Triangle B A C is similar to triangle E F D
Triangle B A C is similar to triangle E D F
Triangle A B C is similar to triangle D E F
Triangle A B C is similar to triangle D F E
Triangle A B C is similar to triangle D E F. Triangle C B A is similar to triangle F D E (order reversed).
To determine if the triangles could be similar, we need to compare the ratios of their corresponding side lengths.
For Triangle RST:
- Side RS is 3 centimeters
- Side ST is 6 centimeters
- Side RT is 8 centimeters
For Triangle WXU:
- Side WX is 18 centimeters
- Side XU is 7.5 centimeters
- Side WU is 15 centimeters
To find the common ratio, we can divide the lengths of the corresponding sides:
For Triangle RST, the ratio of side RS to side ST is 3/6 = 0.5
For Triangle RST, the ratio of side RS to side RT is 3/8 = 0.375
For Triangle WXU, the ratio of side WX to side XU is 18/7.5 = 2.4
For Triangle WXU, the ratio of side WX to side WU is 18/15 = 1.2
Therefore, none of the statements accurately describe the triangles. The common ratio between the triangles is neither 3 nor 2.5. The triangles could not be similar as the ratios of the side lengths are not consistent.
To determine if two triangles can be similar based on their side lengths, we need to check if their ratios of corresponding side lengths are equal.
For Triangle RST, the ratio of side RS to side ST is 3/6 = 1/2, and the ratio of side RS to side RT is 3/8 = 3/8.
For Triangle WXU, the ratio of side WX to side XU is 18/7.5 = 12/5 = 2.4, and the ratio of side WX to side WU is 18/15 = 6/5 = 1.2.
Since the ratios of the side lengths of Triangle RST and Triangle WXU are not equal, the triangles could not be similar.
Therefore, the statements that accurately describe the triangles are:
- The triangles could not be similar.
- The ratios of the side lengths are not consistent.