Which similarity statement is true for a triangle with angles R

Question

, 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∼△CED
triangle upper R upper S upper T tilde 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∼△ECD

Answer 1

To determine the similarity of the triangles, we need to analyze the angles given for both triangles:

For triangle RST:

• \( m∠R = 29° \)
• \( m∠T = 71° \)

To find \( m∠S \):

• The sum of angles in a triangle is 180°.
• Therefore, \( m∠S = 180° - m∠R - m∠T = 180° - 29° - 71° = 80° \).

So, the angles of triangle RST are:

• \( m∠R = 29° \)
• \( m∠S = 80° \)
• \( m∠T = 71° \)

For triangle CDE:

• \( m∠D = 71° \)
• \( m∠C = 80° \)

To find \( m∠E \):

• The sum of angles in a triangle is 180°.
• Therefore, \( m∠E = 180° - m∠C - m∠D = 180° - 80° - 71° = 29° \).

So, the angles of triangle CDE are:

• \( m∠C = 80° \)
• \( m∠D = 71° \)
• \( m∠E = 29° \)

Now we can compare the angles of the two triangles:

• Triangle RST has angles: \( 29° \), \( 80° \), \( 71° \)
• Triangle CDE has angles: \( 29° \), \( 80° \), \( 71° \)

Since both triangles have the same angles, we conclude that:

\[ \triangle RST \sim \triangle CDE \]

Thus, the true similarity statement is:

\[ \triangle RST \sim \triangle CED \] (however, please note that there seems to be a typo because the order matters: it should be \(\triangle RST \sim \triangle CDE\)).

The correct response given the provided options is:

\(\triangle RST \sim \triangle ECD\).