Show the similarity between a triangle with angles A, B, 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°.
The similarity between these two triangles can be demonstrated by comparing their corresponding angles. In both triangles, angle B is equal to angle H (both measuring 36°). This indicates that both triangles have one pair of congruent angles.
However, it is important to note that the other two angles, A and C in the first triangle and G and J in the second triangle, are not congruent. Therefore, these two triangles are not similar. They only share one pair of congruent angles but not all three.
To determine the similarity between two triangles, we need to compare their corresponding angles. If the corresponding angles of two triangles are congruent, then the triangles are similar.
Let's compare the angles of the given triangles:
Triangle 1 with angles A, B, C:
m<A = 47°
m<B = 36°
Triangle 2 with angles G, H, J:
m<G = 36°
m<J = 97°
From the given information, we can see that angle B in Triangle 1 is congruent to angle G in Triangle 2 (both measuring 36°).
However, we do not have any information to determine whether angle C in Triangle 1 is congruent to any angle in Triangle 2.
Therefore, based on the given information, we cannot determine the similarity between the two triangles as the angles are not fully congruent.