In triangle ABC, if angle A = 90 degrees and AB = AC, what type of triangle is A

₹0.0

Question: In triangle ABC, if angle A = 90 degrees and AB = AC, what type of triangle is ABC?

Options:

Correct Answer: Isosceles

Solution:

Triangle ABC is an isosceles right triangle because it has two equal sides and one right angle.

In triangle ABC, if angle A = 90 degrees and AB = AC, what type of triangle is ABC?

In triangle ABC, if angle A = 90 degrees and AB = AC, what type of triangle is ABC?

Step 1: Identify the given information. We have triangle ABC with angle A equal to 90 degrees and sides AB and AC.
Step 2: Understand what angle A being 90 degrees means. This means triangle ABC has a right angle.
Step 3: Recognize that AB = AC means that two sides of the triangle are equal in length.
Step 4: Recall the definition of an isosceles triangle. An isosceles triangle has at least two sides that are equal.
Step 5: Combine the information. Since triangle ABC has a right angle (90 degrees) and two equal sides (AB and AC), it fits the definition of an isosceles right triangle.
Step 6: Conclude that triangle ABC is an isosceles right triangle.

Triangle Classification – Understanding the properties of triangles, specifically isosceles and right triangles.
Angle Properties – Recognizing that a triangle with one 90-degree angle is a right triangle.
Side Length Relationships – Identifying that equal side lengths indicate an isosceles triangle.