Question: In triangle ABC, if angle A = 90 degrees and AB = AC, what type of triangle is ABC?
Options:
Scalene
Isosceles
Equilateral
Right
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 A
Practice Questions
Q1
In triangle ABC, if angle A = 90 degrees and AB = AC, what type of triangle is ABC?
Scalene
Isosceles
Equilateral
Right
Questions & Step-by-Step Solutions
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 β Understanding the properties of triangles, specifically isosceles and right triangles.
Angle Properties β Recognizing that a triangle with one 90-degree angle is a right triangle.
Side Length Relationships β Identifying that equal side lengths indicate an isosceles triangle.
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