Are all isosceles triangles similar? Are all right triangle similar? Are all isosceles right triangles similar? Explain.
1 answer:
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Answer:
a) no
b) no
c) yes
Step-by-step explanation:
a) Isosceles triangles can have a third angle (the one that is not part of the pair of equal angles) with any value in the range 0 < α < 180°. Triangles with different angle values will not be similar.
Not all isosceles triangles are similar.
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b) The smallest acute angle of a right triangle can have any measure in the range 0 < α ≤ 45°. Right triangles having different smallest angles will not be similar. The attachment shows dissimilar right triangles.
Not all right triangles are similar.
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c) If the smallest acute angle of a right triangle is 45°, then both acute angles are 45°, and the right triangle is an isosceles triangle. Each such triangle will be similar to every such triangle.
All isosceles right triangles are similar.
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