Ask a New Question
Menu

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 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≅△CED triangle upper R upper S upper T congruent to triangle upper C upper E upper D Remaining Attempts : 3

1 answer

To determine which similarity statement is true, we first need to find the measure of angle S in triangle RST and angle E in triangle CDE.

Given:

  • In triangle RST:
    • m∠R = 29°
    • m∠T = 71°

We can find m∠S: \[ m∠S = 180° - m∠R - m∠T = 180° - 29° - 71° = 80° \]

So, the measures of the angles in triangle RST are:

  • m∠R = 29°
  • m∠S = 80°
  • m∠T = 71°

Now, in triangle CDE:

  • m∠D = 71°
  • m∠C = 80°

We can find m∠E: \[ m∠E = 180° - m∠C - m∠D = 180° - 80° - 71° = 29° \]

So, the measures of the angles in triangle CDE are:

  • m∠C = 80°
  • m∠D = 71°
  • m∠E = 29°

Now we can compare the angles in both triangles:

  • Triangle RST has angles 29°, 80°, and 71°.
  • Triangle CDE has angles 29°, 80°, and 71°.

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

The correct similarity statement is: \[ \triangle RST \sim \triangle CDE. \]

Thus, the response is: △RST∼△CED.