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Which statements about triangle QRS are true? Select three options. …

Mathematics Questions

Which statements about triangle QRS are true? Select three options. 1. The side opposite ‚a†Q is RS. 2. The side opposite ‚a†R is RQ. 3. The hypotenuse is QR. 4. The side adjacent to ‚a†R is SQ. 5. The side adjacent to ‚a†Q is QS.

Short Answer

The opposite side of angle Q in triangle QRS is segment RS, while the adjacent side is segment QS. Additionally, for angle R, the sides adjacent are RQ and RS, and SQ does not qualify as adjacent; these observations help clarify the relationships within the triangle.

Step-by-Step Solution

Step 1: Identify the Opposite Side

To understand the properties of triangle QRS, we start by determining the opposite side of angle Q. The side that does not touch angle Q but is across from it is called the opposite side. In this case, it is the segment RS. Visualizing the triangle clearly shows that RS is opposite Q, confirming that this statement is true.

Step 2: Analyze the Adjacent Side

The next step is to find the adjacent side to angle Q. The adjacent side is one that connects at angle Q and is not the hypotenuse. In triangle QRS, the segment QS runs alongside angle Q and thus qualifies as the adjacent side. This observation leads us to conclude that the statement regarding QS being adjacent to Q is indeed true.

Step 3: Examine Other Relationships

Lastly, it’s crucial to assess the other relationships in the triangle. Here, we should look at the adjacent side to angle R and confirm the hypotenuse. The hypotenuse is generally the longest side in a right triangle but cannot be recognized here as the triangle type is unspecified. Also, we need to note that contrary to claims, sides adjacent to angle R are RQ and RS while SQ does not qualify as adjacent. Thus, we identify which statements are true or false based on these clarifications.

Related Concepts

Opposite Side

The side of a triangle that is across from a given angle and does not touch that angle

Adjacent Side

The side of a triangle that forms one of the angles in question and is not the hypotenuse

Hypotenuse

The longest side of a right triangle, opposite the right angle, but may depend on the triangle’s classification.