The Isosceles Triangle: Its Congruent Legs And Base Angles

Base angles of an isosceles triangle Chapter 5 (p. 244)

The two angles adjacent to the base of an isosceles triangle

An isosceles triangle is a triangle in which two of the sides (called legs) are congruent, which means they have the same length. The third side (called the base) is of a different length.

Since an isosceles triangle has two congruent legs, it also has two congruent base angles. These angles are the angles that are opposite to the congruent legs.

To prove this, we can use the following reasoning:

– In an isosceles triangle, the two legs have the same length. Let’s call this length x.
– Because the sum of the measures of the angles in a triangle is 180 degrees, we can write the equation: angle A + angle B + angle C = 180, where A, B, and C are the angles of the triangle.
– Since angles A and B are congruent (they are the base angles), we can write: angle A = angle B = y, where y represents the measure of each base angle.
– Substituting in the angles and simplifying, we get: y + y + angle C = 180.
– Solving for angle C, we get: angle C = 180 – 2y.

Therefore, we can conclude that in an isosceles triangle, the base angles (angles opposite the congruent legs) are congruent, and their measures can be found by using the equation: angle C = 180 – 2y, where y is the measure of each base angle.

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