Concept Check Classify each triangle as acute, right, or obtuse. ...

Question

Concept Check Classify each triangle as acute, right, or obtuse. Also classify each as equilateral, isosceles, or scalene. See the discussion following Example 2.

Accepted Answer

Hello. Today, we're going to be identifying whether the given triangle is an acute, right or obtuse triangle. And we'll be categorizing it as a equilateral isosceles or scaling triangle. So we are given a triangle ABC, we are told that two sides of the triangle are equivalent to each other and two angles are given to us at 65 degrees. Now, let's go ahead and start by determining whether the triangle is acute right or obtuse. Now, in order to determine this, we'll need to find all three angles, we are given two of the angles at 65 degrees, but we'll need to find the third missing angle. In order to do that, we can use the addition angle property for triangles. The property states that the sum of all three angles in a triangle must add up to 180 degrees. So in order to find the missing angle, A, we can add the three angles which is angle A plus angle B which is 65 degrees plus angle C which is also 65 degrees and set equal to 180 degrees. Now 65 plus 65 will give us the value of 130. So we have a plus 130 degrees is equal to 180 degrees. And finally, in order to solve for angle A, we're going to subtract 130 degrees from both sides of the equation that will leave us with a final angle A which is equal to degrees. So we know that the third angle is 50 degrees. And one thing to note is that angle A angle B and angle C are all less than 90 degrees. Since these V, these three angles are less than 90 degrees, this is showing that this is going to be an acute angle or an acute triangle. Since all three angles of the triangle are acute. Now that we know that this is an acute triangle, we need to classify the triangle as equilateral isosceles or scale. Now we are told that the triangle has two equivalent sides. The definition for an isosceles triangle is any triangle that has two equivalent sides. Therefore, we are going to categorize this triangle as an isosceles triangle. So we know that the triangle isosceles and the triangle is an acute triangle. Therefore, the answer to this problem is going to be a. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

Concept Check Classify each triangle as acute, right, or obtuse. Also classify each as equilateral, isosceles, or scalene. See the discussion following Example 2.

Key Concepts

Types of Angles

Types of Triangles by Sides

Triangle Inequality Theorem

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