In triangle XYZ, if angle X = 45 degrees and angle Y = 45 degrees, what is the r

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Question: In triangle XYZ, if angle X = 45 degrees and angle Y = 45 degrees, what is the ratio of the sides opposite to these angles? (2021)

Options:

Correct Answer: 1:1

Exam Year: 2021

Solution:

In an isosceles triangle with angles 45-45-90, the sides opposite the equal angles are equal, hence the ratio is 1:1.

In triangle XYZ, if angle X = 45 degrees and angle Y = 45 degrees, what is the ratio of the sides opposite to these angles? (2021)

In triangle XYZ, if angle X = 45 degrees and angle Y = 45 degrees, what is the ratio of the sides opposite to these angles? (2021)

Step 1: Identify the triangle XYZ and the given angles. We have angle X = 45 degrees and angle Y = 45 degrees.
Step 2: Recognize that in triangle XYZ, since angle X and angle Y are both 45 degrees, this is an isosceles triangle.
Step 3: In an isosceles triangle, the sides opposite the equal angles are also equal.
Step 4: Since angle X and angle Y are both 45 degrees, the sides opposite these angles (let's call them side x and side y) are equal.
Step 5: Therefore, the ratio of the sides opposite to angles X and Y is 1:1.

Triangle Properties – Understanding the properties of isosceles triangles and the relationship between angles and opposite sides.
Angle Sum Property – Applying the angle sum property of triangles to deduce the third angle.
Special Triangles – Recognizing the characteristics of 45-45-90 triangles and their side ratios.