Question

Which similarity statement is true for a triangle with angles R
, S
, and T
(where m∠R=29°
and m∠T=71°
) and another triangle with angles C
, D
, and E
(where m∠D=71°
and m∠C=80°
)?(1 point)
Responses

△RST∼△ECD
triangle upper R upper S upper T tilde triangle upper E upper C upper D

△RST≅△CED
triangle upper R upper S upper T congruent to triangle upper C upper E upper D

△RST≅△ECD
triangle upper R upper S upper T congruent to triangle upper E upper C upper D

△RST∼△CED

Answer 1

To determine the similarity statement between triangles \( RST \) and \( CDE \), we first need to find the measures of the angles of triangle \( RST \) and triangle \( CDE \).

For triangle \( RST \):
- \( m∠R = 29° \)
- \( m∠T = 71° \)
- Therefore, \( m∠S = 180° - m∠R - m∠T = 180° - 29° - 71° = 80° \).

So the angles in triangle \( RST \) are:
- \( m∠R = 29° \)
- \( m∠S = 80° \)
- \( m∠T = 71° \)

For triangle \( CDE \):
- \( m∠D = 71° \)
- \( m∠C = 80° \)
- Therefore, \( m∠E = 180° - m∠C - m∠D = 180° - 71° - 80° = 29° \).

So the angles in triangle \( CDE \) are:
- \( m∠C = 80° \)
- \( m∠D = 71° \)
- \( m∠E = 29° \)

Now, we can compare the angles:
- Triangle \( RST \): \( m∠R = 29° \), \( m∠S = 80° \), \( m∠T = 71° \)
- Triangle \( CDE \): \( m∠C = 80° \), \( m∠D = 71° \), \( m∠E = 29° \)

The angles of both triangles are equal:
- \( m∠R = m∠E \)
- \( m∠S = m∠C \)
- \( m∠T = m∠D \)

Since all corresponding angles are equal, the triangles are similar.

Thus, the correct similarity statement is:
\[
\triangle RST \sim \triangle CED
\]

So the correct answer from the provided options is:
**△RST∼△CED.**