In each of two right triangles, one angle measure is two times another angle measure. Are the triangles similar? Explain your reasoning.
Answer (3)
No, because it is twice the size of the opposite angle, one is larger than the other.
What is the similarity law for triangles?
Although it is not required that the two **triangles **be the same size, it is required by law to demonstrate that they have the same form. The respective sides' ratios are equal in size , and the corresponding angles are congruent .
It is given that the two right triangles ' one angle measure is two times another angle.
We have to find the similarity relation.
Since only one **angle **is two the measure of one of the other angles. The similarity rules will not be followed.
Thus, the triangles are not similar .
Learn more about the** similarity of triangles** here:
brainly.com/question/8045819
#SPJ2
To determine if two right triangles are similar, we must show that they have all corresponding angles equal. If one angle in each triangle is twice the measure of another angle, this condition alone does not necessarily make the triangles similar. In a right triangle, we know one angle is 90 degrees.
Therefore, if in both triangles one of the acute angles is double the other, the set of angles for each triangle could be 90 degrees, 30 degrees, and 60 degrees. According to the Angle-Angle (AA) Similarity Postulate, two triangles are similar if they have two corresponding angles that are equal.
Since the third angle is determined by the first two (as the sum of angles in a triangle is always 180 degrees), having two equal angles is sufficient for triangle similarity. In our case, since both triangles would have angles of 90 degrees, 30 degrees, and 60 degrees, they are indeed similar triangles.
Yes, the two right triangles are similar because they have corresponding angles that are equal. This is due to one angle being twice another, which gives angles of 30°, 60°, and 90° in both triangles. By the AA criterion for similarity, the triangles are confirmed to be similar.
;
