Which of the following statement is false?
(a) All isosceles triangles are similar.
(b) All equilateral triangles are similar.
(c) All circles are similar.
(d) None of the above
Answers
(a) All isosceles triangles are similar - untrue
Step-by-step explanation:
Statement A is False.
All isosceles triangles are not similar.
An isosceles triangle is one in which 2 out of the 3 sides are equal in length and that their 2 base angles are equal. Two isosceles triangles can individually have two sides equal, but they may not be similar as their sides could be of different measurement.
Equilateral triangles are similar and all circles are similar.
Given : Few statements
To Find : Which of the following statement is false?
(a) All isosceles triangles are similar.
(b) All equilateral triangles are similar.
(c) All circles are similar.
(d) None of the above
Solution:
(a) All isosceles triangles are similar.
This is False
For example two triangles with sides
3 , 3 , 4 and 3 , 3 , 5
both are isosceles but not similar
Hence All isosceles triangles are similar. is FALSE
3/3 = 3/3 ≠ 4/5
All equilateral triangles are similar.
TRUE
as All three angles of equilateral triangles are 60°
Hence corresponding angles of equilateral triangles are equal
so Similar
TRUE
All circles are similar. = TRUE
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