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Answered

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Can a triangle be both acute and isosceles? Justify your reasoning.

Sagot :

perezkhristine

Answer:

No. There can be an obtuse angle or a right-angle in an isosceles triangle.

Step-by-step explanation:

Explanation:

No. You can three types of isosceles triangles:

acute-angled isosceles triangle

All the angles are acute and the base angles are equal.

eg:  

75 ° , 75 ° , 30 °

 or  

50 ° , 50 ° , 80 °

right-angled isosceles triangle

One angle is  90 °  and the other two are both  45 °

45 ° , 45 ° , 90 °

   ←    

(like one of the usual set squares)

obtuse-angles isosceles triangle

One angle is obtuse and the base angles are equal.

eg:  

30 ° , 30 ° , 120 °

 or  

25 ° , 25 ° , 130 °

Ofcourse there can only be one  90 °

or

one obtuse angle in a triangle. The other two angles MUST be acute, else the sum would be more than  180 °

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