Respuesta :
Answer:
- A and B
- C and D
Step-by-step explanation:
Triangles are similar when they have angles with the same measure. Since the sum of angles is 180°, the three angles will have the same measure if any two have the same measure.
Triangles A and B
The given two angles have the same measure, so all three angles have the same measure. Triangles A and B are similar.
Triangles C and D
The third angle of Triangle C has measure ...
180° -90° -37° = 53°
Hence two of the angles of Triangle C match the given angles of Triangle D, so all three angles have the same measure. Triangles C and D are similar.
Triangles E and F
Neither of the angles of Triangle E match either of the given angles of Triangle F, so the triangles cannot be similar.
Triangles G and H
The sum of the remaining angles of Triangle G must be less than 59°, so neither angle can be 70°. The triangles cannot be similar.
The similarity of two triangles depends on the equality of the corresponding angles and the proportionality of the corresponding sides
The correct options are;
- Triangle A: 53, 71, Triangle B: 53, 71; Similar
- Triangle C: 90, 37, Triangle D: 90, 53; Similar
- Triangle E: 63, 45 Triangle F:14, 71; Not similar
- Triangle G, 121, Triangles H: 70, Not similar
Reason:
In the event that two angles of one triangle are congruent to two of the
angles of another triangle, then the two triangles are similar according to
Angle Angle, AA, similarity postulate
The AA similarity postulate is correct given that the sum of the interior
angles of a triangle is 180° by the angle sum property of a triangle,
therefore, where two angles are congruent, the third angle is also
congruent
- Triangle A: 53, 71, Triangle B: 53, 71; Similar
The triangles are similar by AA similarity postulate
- Triangle C: 90, 37, Triangle D: 90, 53; Similar
The triangle are similar, given that the the given angles are equal to each of their complementary angles
- Triangle E: 63, 45 Triangle F:14, 71; Not similar
The triangles are not similar
- Triangle G, 121, Triangles H: 70, Not similar
The information is not sufficient
Learn more about AA similarity postulate here:
https://brainly.com/question/11289488
