QQuestionMathematics
QuestionMathematics
Triangle Inequality Theorem 2 (Aa → Ss) - if one angle of a triangle is larger than a second angle, then the side opposite the first angle is longer than the side opposite the second angle.
Example: Figure 2 shows a triangle with angles of different measures. List all sides of Figure 2 in ascending order.
Solution:
By the Triangle Inequality Theorem 2, *R* is a largest angle, that follows the opposite side QS is the longest side. Also, since *Q* is the smallest angle, then the opposite side *R* is the shortest side. Hence, *R*S-QR-QS.
12 months agoReport content
Answer
Full Solution Locked
Sign in to view the complete step-by-step solution and unlock all study resources.
Step 1:: Identify the longest side of the triangle.
QS\text{ is the longest side.}
By the Triangle Inequality Theorem 2 (Aa → Ss), if one angle of a triangle is larger than a second angle, then the side opposite the first angle is longer than the side opposite the second angle.
Step 2:: Identify the shortest side of the triangle.
RS\text{ is the shortest side.}
Again, using the same theorem, if an angle is the smallest angle in a triangle, then the side opposite that angle is the shortest side.
Step 3:: Determine the order of the sides from shortest to longest.
RS < QR < QS
Now that we have identified the shortest and longest sides, we can deduce the order of the sides from shortest to longest. Therefore, the sides of the triangle are in the following order:
Final Answer
The sides of the triangle in ascending order are $RS$, $QR$, and $QS$.
Need Help with Homework?
Stuck on a difficult problem? We've got you covered:
- Post your question or upload an image
- Get instant step-by-step solutions
- Learn from our AI and community of students