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

△RST∼△CED

Answer 1

To determine which similarity statement is true for the triangles given their angles, we first need to find the measure of angle \( S \) in triangle \( RST \) and angle \( E \) in triangle \( CDE \).

For triangle \( RST \):

• \( m\angle R = 29^\circ \)
• \( m\angle T = 71^\circ \)

To find \( m\angle S \): \[ m\angle S = 180^\circ - m\angle R - m\angle T = 180^\circ - 29^\circ - 71^\circ = 80^\circ \]

So, we have \( m\angle R = 29^\circ \), \( m\angle S = 80^\circ \), and \( m\angle T = 71^\circ \).

Now for triangle \( CDE \):

• \( m\angle D = 71^\circ \)
• \( m\angle C = 80^\circ \)

To find \( m\angle E \): \[ m\angle E = 180^\circ - m\angle C - m\angle D = 180^\circ - 80^\circ - 71^\circ = 29^\circ \]

So, we have \( m\angle C = 80^\circ \), \( m\angle D = 71^\circ \), \( m\angle E = 29^\circ \).

Now, we can compare the angles of both triangles:

• Triangle \( RST \): \( 29^\circ, 80^\circ, 71^\circ \)
• Triangle \( CDE \): \( 29^\circ, 80^\circ, 71^\circ \)

Since both triangles have the same angles, they are congruent, and their angle measures match.

The correct similarity statement is: \[ \triangle RST \sim \triangle CDE \] Thus, the correct choice is: △RST∼△CED.