Parts of a Triangle: Classify a triangle by its sides

We are given a triangle ABC with a vertex A, and it is noted that AD is both the height from A to the base BC and the median of the triangle. Let's analyze the situation:

• Step 1: Since AD is the height, it is perpendicular to the base BC. This tells us that the line AD forms a right angle with BC.
• Step 2: Being a median indicates that AD also bisects BC, meaning B and C are equidistant from D. Therefore, $BD = DC$.
• Step 3: The dual role of AD — both a height and a median — is critical. In triangles, if a line segment from a vertex also serves as both a height and a median, the triangle is isosceles. This is due to the symmetry introduced by these properties.
• Step 4: Correctly, this means two sides of triangle ABC must be equal. Specifically, since AD meets BC at its midpoint and is also perpendicular, this symmetry means side AB is equal to side AC.

Thus, triangle ABC must be isosceles. This perfectly fits the conventional definition where two sides of the triangle are equal and aligns with the properties of a line being both a height and a median.

Therefore, the solution to the problem is Isosceles.

To classify the triangle, observe that all three sides are equal as given by $AB = AC = BC$. This equality of all three sides fits the definition of an equilateral triangle, which is a triangle where all sides have the same length.

Thus, the type of triangle is equilateral.

To classify the triangle, we must examine its properties based on its sides.

• An equilateral triangle has all three sides of equal length.
• An isosceles triangle has two sides of equal length.
• A scalene triangle, informally called a generic triangle, has all sides of different lengths.

Without specific information about the side lengths from the given diagram or description, we assume no notable equalities among the sides.

Given that no equal sides are indicated, and the triangle would not spontaneously denote isosceles or equilateral criteria without specific symbology or markings, the most applicable classification is as a scalene triangle — termed a "generic triangle" in the given options.

Therefore, the type of triangle is a generic triangle.

To solve this problem, we'll follow these steps:

• Step 1: Identify the given information about the triangle.
• Step 2: Use the properties of triangles to classify the triangle based on its sides.

Now, let's work through each step:
Step 1: The problem states that $AB = AC$. This means two sides of the triangle are equal.
Step 2: In triangle classification by sides, if two sides are equal, it is known as an isosceles triangle.

Therefore, the type of triangle we are dealing with here is an isosceles triangle.

The correct multiple-choice selection is: Isosceles (choice ID 2).

To solve this problem, we'll follow these steps:

• Step 1: Identify the given information
• Step 2: Apply the properties of triangles to classify it

Now, let's work through each step:
Step 1: The triangle is given with sides $AB$ and $BC$ equal in length.
Step 2: According to the properties of triangles, a triangle with at least two equal sides is classified as an isosceles triangle.
Therefore, given that $AB = BC$, the triangle is an Isosceles triangle.

Therefore, the solution to the problem is Isosceles.