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Which statement proves that the angle of triangle ABC are congruent?

Which statement proves that the angle of triangle ABC are congruent?-example-1
User Ntm
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1 Answer

20 votes
20 votes

Let's examine the options to look for the right one.

The first option is incorrect. If two sides of a triangle are congruent, then the other two angles are congruent. But that angle between those congruent sides can have any measure.

The second option is a definition of an equilateral triangle. Therefore, it doesn't prove that the angles are all congruent.

The third option shows two statements that don't depend on each other because the angles of any triangle will sum up to 180º.

The fourth option is true, as we have said before. So, if we use this statement for each pair of adjacent sides, we can prove that the Triangle ABC have congruent angles:

sides AB and AC are congruent => angles C and B are congruent

sides AC and CB are congruent => angles B and A are congruent

Then, C ≅ B ≅ A.

Therefore, the correct statement is the last one.

User Chris Watts
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