applying the triangle inequality theorems and the converse of the pytha…
Triangle JKL is obtuse triangle. Triangle XYZ is acute triangle.
Question
applying the triangle inequality theorems and the converse of the pythagorean theorem
classify each of the triangles as acute, obtuse, or right.
triangle jkl is □ triangle.
triangle xyz is □ triangle.
triangle jkl has side lengths: jk=4, jl=6, kl=3
triangle xyz has side lengths: xz=4, zy=4, xy=5
Solution Steps
-
Understand the question
applying the triangle inequality theorems and the converse of the pythagorean theorem
classify each of the triangles as acute, obtuse, or right.
triangle jkl is □ triangle.
triangle xyz is □ triangle.
triangle jkl has side lengths: jk=4, jl=6, kl=3
triangle xyz has side lengths: xz=4, zy=4, xy=5 -
Explanation
Step1: Classify △JKL
Let \(a=3\), \(b=4\), \(c=6\) (longest side).
Compare \(a^2 + b^2\) vs \(c^2\):
\(3^2 + 4^2 = 9 + 16 = 25\)
\(6^2 = 36\)
Since \(25 < 36\), \(a^2 + b^2 < c^2\).Step2: Classify △XYZ
Let \(a=4\), \(b=4\), \(c=5\) (longest side).
Compare \(a^2 + b^2\) vs \(c^2\):
\(4^2 + 4^2 = 16 + 16 = 32\)
\(5^2 = 25\)
Since \(32 > 25\), \(a^2 + b^2 > c^2\). -
Final answer
Triangle JKL is obtuse triangle.
Triangle XYZ is acute triangle.
Answer
Explanation
Step1: Classify △JKL
Let \(a=3\), \(b=4\), \(c=6\) (longest side).
Compare \(a^2 + b^2\) vs \(c^2\):
\(3^2 + 4^2 = 9 + 16 = 25\)
\(6^2 = 36\)
Since \(25 < 36\), \(a^2 + b^2 < c^2\).
Step2: Classify △XYZ
Let \(a=4\), \(b=4\), \(c=5\) (longest side).
Compare \(a^2 + b^2\) vs \(c^2\):
\(4^2 + 4^2 = 16 + 16 = 32\)
\(5^2 = 25\)
Since \(32 > 25\), \(a^2 + b^2 > c^2\).
Answer
Triangle JKL is obtuse triangle.
Triangle XYZ is acute triangle.
Question Image
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Subject
mathematics
Sub Subject
geometry
Education Level
high school
Difficulty
unspecified
Question Type
with image, calculation
Multi Question
No
Question Count
1
Analysis Status
completed
Analyzed At
2026-02-09T20:07:55
OCR Text
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applying the triangle inequality theorems and the converse of the pythagorean theorem classify each of the triangles as acute, obtuse, or right. triangle jkl is □ triangle. triangle xyz is □ triangle. triangle jkl has side lengths: jk=4, jl=6, kl=3 triangle xyz has side lengths: xz=4, zy=4, xy=5
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