Question

geometry with data analysis ic qtr b young continuous learning center - credit bearing (tutor)
isosceles triangles
identifying isosceles triangle properties
which properties belong to all isosceles triangles? choose three correct answers.
the two sides opposite the base angles are congruent.
all three angles are congruent.
the base angles are congruent.
the bisector of the vertex angle is the perpendicular bisector of the base.
all three sides are congruent.

Explanation:

• "The two sides opposite the base angles are congruent": In an isosceles triangle, by definition, two sides are equal. If we consider the base angles (the angles opposite the equal sides), the sides opposite them (the other two sides) are congruent.
• "The base angles are congruent": This is a fundamental property of isosceles triangles (the Isosceles Triangle Theorem).
• "The bisector of the vertex angle is the perpendicular bisector of the base": In an isosceles triangle, the angle bisector of the vertex angle also acts as the median (divides the base into two equal parts) and the altitude (is perpendicular to the base), so it is the perpendicular bisector of the base.

• "All three angles are congruent": This is a property of equilateral triangles (a special case of isosceles triangles, but not all isosceles triangles have all three angles congruent).
• "All three sides are congruent": This is a property of equilateral triangles, not all isosceles triangles.

Answer:

• The two sides opposite the base angles are congruent.
• The base angles are congruent.
• The bisector of the vertex angle is the perpendicular bisector of the base.