Question

Show the similarity between a triangle with angles A , B , and C , where m∠A=47° and m∠B=36° , and another triangle with angles G , H , and J , where m∠G=36° and m∠J=97° .(1 point)

△ABC∼△GHJ
△ABC∼△HGJ
△ABC∼△GJH
△ABC∼△HJG

Answer 1

To determine the similarity between the two triangles, we need to find the missing angles of each triangle and then compare the angle measures.

For triangle ABC:
- Given: m∠A = 47° and m∠B = 36°
- To find m∠C:
\[
m∠C = 180° - m∠A - m∠B = 180° - 47° - 36° = 97°
\]

So the angles of triangle ABC are:
- m∠A = 47°
- m∠B = 36°
- m∠C = 97°

For triangle GHJ:
- Given: m∠G = 36° and m∠J = 97°
- To find m∠H:
\[
m∠H = 180° - m∠G - m∠J = 180° - 36° - 97° = 47°
\]

So the angles of triangle GHJ are:
- m∠G = 36°
- m∠H = 47°
- m∠J = 97°

Now we can compare the angles of both triangles:
- Triangle ABC: 47°, 36°, 97°
- Triangle GHJ: 36°, 47°, 97°

Since the angles in both triangles are the same (regardless of the order), we can conclude that:

\[
△ABC \sim △GHJ
\]

Thus, the answer is:
**△ABC∼△GHJ**