If Triangle M N O is congruent to triangle N M O, what statement best describes triangle MON?
The triangle is scalene.
The triangle is equilateral.
The triangle is isosceles and possibly equilateral.
The triangle is isosceles but definitely not equilateral.
Answers
If Triangle M N O is congruent to triangle N M O, what statement best describes triangle MON?
A - The triangle is scalene.
B - The triangle is equilateral.
C - The triangle is isosceles and possibly equilateral.
D - The triangle is isosceles but definitely not equilateral.
Answer:
The triangles have the same size and shape, it follows that all three sides of triangle MON are congruent. This means that triangle MON is an equilateral triangle. Therefore, the statement that best describes triangle MON is (B) - The triangle is equilateral.
Explanation:
If Triangle MNO is congruent to triangle NMO, it means that the two triangles have the same size and shape, but their vertices are ordered differently. In other words, the corresponding sides and angles of the triangles are congruent.
An equilateral triangle is a special case of an isosceles triangle, where all sides and angles are equal. However, an isosceles triangle only requires two sides to be equal. Therefore, statement (C) - The triangle is isosceles and possibly equilateral - is incorrect, since an equilateral triangle is always isosceles, but not all isosceles triangles are equilateral.
Statement (D) - The triangle is isosceles but definitely not equilateral - is also incorrect because triangle MON is, in fact, equilateral.
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