California Assessment of Student Performance and Progress (CAASPP) Math Practice Exam

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In which type of triangle do the angles opposite the two congruent sides share equal measures?

Isosceles Triangle
Equilateral Triangle
Right Triangle
Scalene Triangle

The correct answer is: Isosceles Triangle

An isosceles triangle is characterized by having at least two congruent sides. The fundamental property of an isosceles triangle is that the angles opposite these two congruent sides are equal in measure. This means that if you know one of the angles formed by the base of the triangle, you can determine the other angle because they are congruent. In this type of triangle, the relationship between its sides and angles is crucial, as it helps in calculating unknown measures when some dimensions are given. This property of equal angles enables the understanding of various geometrical concepts and theories, making the isosceles triangle a significant figure in geometry. While an equilateral triangle is another special type where all sides and angles are equal, the question specifically asks about the equality of angles opposite congruent sides, which directly pertains to the definition of isosceles triangles. A right triangle has one angle measuring 90 degrees, and a scalene triangle has all sides of different lengths and, consequently, all angles of different measures, neither of which relate to the congruent side property of the isosceles triangle.