In ∆RST, RS = 10, RT = 15, and m∠R = 32. In ∆UVW, UV = 12, UW = 18, and m∠U = 32.
Which of the following statements is correct?
1. ∆RST ∼ ∆WUV and the similarity ratio is 56.
2. ∆RST ∼ ∆UVW and the similarity ratio is 56.
3. ∆RST ∼ ∆VWU and the similarity ratio is 65.
4. The triangles are not similar.
2. and the ratio is 5:6
what is the name of a quadrilateral with one pair of opposites sides parallel?
To determine if the triangles are similar, we need to compare the lengths of corresponding sides and the measures of corresponding angles.
Given information:
∆RST: RS = 10, RT = 15, m∠R = 32
∆UVW: UV = 12, UW = 18, m∠U = 32
To check if the triangles are similar, we can compare the ratios of the side lengths.
For ∆RST and ∆UVW:
RS/UV = 10/12 = 5/6
RT/UW = 15/18 = 5/6
The ratios of the side lengths are equal, indicating that the triangles may be similar.
Now let's compare the angles.
For ∆RST and ∆UVW:
m∠R = m∠U = 32
The angles are equal, indicating that the triangles may be similar.
Therefore, the correct statement is:
2. ∆RST ∼ ∆UVW and the similarity ratio is 56.
To determine which statement is correct, we need to examine the given information about ∆RST and ∆UVW and compare their corresponding sides and angles.
Let's first compare the corresponding angles. We are given that m∠R = 32 and m∠U = 32. Since the angles are equal, the triangles have a pair of congruent angles.
Now let's compare the corresponding sides. We have RS = 10, RT = 15, UV = 12, and UW = 18. Comparing the ratios of the corresponding sides, we can calculate:
RS/UV = 10/12 ≈ 0.833
RT/UW = 15/18 ≈ 0.833
If the ratios of the corresponding sides are equal, then the triangles are similar.
From our calculations, we see that the ratio of the corresponding sides is approximately 0.833 for both RS/UV and RT/UW. This means that the ratio of the corresponding sides is NOT 56 or 65.
Therefore, the correct statement is:
4. The triangles are not similar.