contestada

Which pair of triangles are similar?
A
Triangles 1 and 2 each have a 36° angle.
a
B
Triangles 3 and 4 each have a 42° angle.
с
Triangle 5 has a 70 angle and a 95° angle. Triangle 6 has a 30° and a 75º.
a
D
Triangle 7 has a 30 angle and a 90°. Triangle 6 has a 30° and a 60°.

Respuesta :

Ankit

Answer:

[tex] \sf \fbox{Option D have pair of triangles are similiar}[/tex]

Step-by-step explanation:

To prove triangles are pair we will use AAA property.

ln option A the given triangles 1 & 2 have a 36° Angle, but the remaining two angles of both the traingle are not mentioned, as long as we don't know the measure of other two angle of both the traingle we can't say that pair of triangles are similar.

Similarly In option B triangles 3 & 4 can't be pair of similar triangle

In option C triangle 5 & 6 don't have any common angle, hence it does not follows AAA property and the given pair of traingles are not similar.

In option D Two angles of each triangle are given so we can easily find the third angle of both the triangle. let's solve for the third angles of triangle 7 and 8.

in triangle 7,

  • given angles are 30° and 90°
  • let the third angle be X,
  • now,
  • 30+90+X = 180
  • (sum of all angles of triangle is 180)
  • X= 180-90-30
  • X= 60

All three angles of triangle 7 are 30, 60 & 90

Now in triangle 8,

  • given angles are 30° and 60°
  • let the third angle be Y,
  • now,
  • 30+60+Y = 180
  • (sum of all angles of triangle is 180)
  • Y= 180-90
  • Y= 90

All three angles of triangle 8 are 30, 60 & 90

Hence, both the triangles have same measure of all three angles we can say that triangle 7 & 8 are similar triangle.

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