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Question Video: Identifying the Base Angles of an Isosceles Triangle Mathematics • 11th Grade

In the following triangle, ๐ด๐ต = 3 cm, ๐ต๐ถ = 3 cm, and ๐ด๐ถ = 4 cm. Identify the base angles of this triangle.

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Video Transcript

In the following triangle, ๐ด๐ต equals three centimeters, ๐ต๐ถ equals three centimeters, and ๐ด๐ถ equals four centimeters. Identify the base angles of this triangle. Option (A) angle ๐ด and angle ๐ต. Option (B) angle ๐ด and angle ๐ถ. Or option (C) angle ๐ถ and angle ๐ต.

In this triangle ๐ด๐ต๐ถ, we can identify that there are two sides of length three centimeters and one side of length four centimeters. Recall that an isosceles triangle is a triangle that has two congruent sides. So that means that triangle ๐ด๐ต๐ถ here is an isosceles triangle. The two congruent sides of the isosceles triangle are called the legs of the triangle. The third side is called the base.

Here, we are asked to identify the base angles of the triangle. So letโ€™s recall what we know about the angles in an isosceles triangle.

The isosceles triangle theorem states that if two sides of a triangle are congruent, then the angles opposite those sides are congruent. The two congruent angles in an isosceles triangle are called the base angles. So the angle opposite this three-centimeter leg at the bottom of the triangle is a base angle. And the angle opposite the other leg is also a base angle. And so we can give the answer that the two base angles of the triangle are angle ๐ด and angle ๐ถ, which was the answer given in option (B).

Here, we were provided with answer options, but of course using three vertices to define either angle would also be valid answers, for example, angle ๐ต๐ด๐ถ or ๐ถ๐ด๐ต for angle ๐ด and angle ๐ด๐ถ๐ต or ๐ต๐ถ๐ด for angle ๐ถ.

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