If isosceles triangle ABC has a 130° angle at vertex B, which statement must be true?
In an isosceles triangle, two sides are equal in length
In an isosceles triangle, two sides are equal in length. Let’s consider the given triangle ABC with angle B measuring 130°.
To determine which statement must be true, we need to analyze the properties of isosceles triangles and the given angle.
1. Statement 1: Side AB is longer than sides AC or BC.
This statement is not necessarily true. In an isosceles triangle, the longest side is opposite the largest angle. Since angle B is 130°, we cannot determine the relative lengths of the sides solely based on this information. Therefore, statement 1 is not necessarily true.
2. Statement 2: Angle A and angle C each measure 25°.
In an isosceles triangle, the angles opposite the equal sides are congruent. Since we have an isosceles triangle ABC, and angle B measures 130°, the other two angles (angle A and angle C) must be congruent and equal in measure. Therefore, statement 2 is true. Angle A and angle C each measure 25°.
3. Statement 3: Triangle ABC is an acute triangle.
An acute triangle is a triangle where all angles measure less than 90°. Since we know angle B measures 130°, triangle ABC cannot be an acute triangle. Thus, statement 3 is false. Triangle ABC is not an acute triangle.
To summarize, from the given information, the statement that must be true is statement 2: Angle A and angle C each measure 25°.
More Answers:
The Angle Bisector Theorem and its Converse | Exploring Proportional Segments in Triangles5 Tips for Clear and Concise Math Explanation | Helping Learners Understand
An Introduction to Polyhedra | Understanding the Geometry and Properties of Three-Dimensional Shapes