In triangle ABC, if angle A = 45 degrees and angle B = 45 degrees, what is the r

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Question: In triangle ABC, if angle A = 45 degrees and angle B = 45 degrees, what is the relationship between sides a, b, and c?

Options:

Correct Answer: a = b

Solution:

In an isosceles triangle with angles A and B equal, the sides opposite those angles are equal, hence a = b.

In triangle ABC, if angle A = 45 degrees and angle B = 45 degrees, what is the relationship between sides a, b, and c?

In triangle ABC, if angle A = 45 degrees and angle B = 45 degrees, what is the relationship between sides a, b, and c?

Correct Answer: a = b

Step 1: Identify the triangle ABC and the given angles. We have angle A = 45 degrees and angle B = 45 degrees.
Step 2: Recall that the sum of angles in a triangle is always 180 degrees. So, angle C can be calculated as: angle C = 180 - (angle A + angle B).
Step 3: Substitute the values: angle C = 180 - (45 + 45) = 180 - 90 = 90 degrees.
Step 4: Now we know that triangle ABC has angles of 45 degrees, 45 degrees, and 90 degrees. This means it is a special type of triangle called an isosceles right triangle.
Step 5: In an isosceles triangle, the sides opposite the equal angles are also equal. Here, sides a and b are opposite angles A and B, which are both 45 degrees.
Step 6: Therefore, since angles A and B are equal, the sides opposite them must also be equal. This gives us the relationship: a = b.

Isosceles Triangle Properties – In an isosceles triangle, angles opposite equal sides are equal, and vice versa.
Triangle Angle Sum Theorem – The sum of the angles in a triangle is always 180 degrees.