Question

assignment
3.c.14 practice
#1 - 4
assigned by ashley simeona on
november 12, 2025
1 practice 1
which of the following are right triangles?
a triangle abc with ( ac = 6 ), ( bc = 9 ), and ( ab = 12 )
b triangle def with ( de = 8 ), ( ef = 10 ), and ( df = 13 )
c triangle ghi with ( gi = 9 ), ( hi = 12 ), and ( gh = 15 )
d triangle jkl with ( jk = 10 ), ( kl = 13 ), and ( jl = 17 )
how did i do?

Explanation:

Step1: Recall the Pythagorean theorem

For a right - triangle with sides \(a\), \(b\), and hypotenuse \(c\) (\(c\) is the longest side), \(a^{2}+b^{2}=c^{2}\).

Step2: Check option A

\(AC = 6\), \(BC = 9\), \(AB = 12\).
\(AC^{2}+BC^{2}=6^{2}+9^{2}=36 + 81=117\), \(AB^{2}=12^{2}=144\).
Since \(117
eq144\), triangle \(ABC\) is not a right - triangle.

Step3: Check option B

\(DE = 8\), \(EF = 10\), \(DF = 13\).
\(DE^{2}+EF^{2}=8^{2}+10^{2}=64 + 100 = 164\), \(DF^{2}=13^{2}=169\).
Since \(164
eq169\), triangle \(DEF\) is not a right - triangle.

Step4: Check option C

\(GI = 9\), \(HI = 12\), \(GH = 15\).
\(GI^{2}+HI^{2}=9^{2}+12^{2}=81+144 = 225\), \(GH^{2}=15^{2}=225\).
Since \(GI^{2}+HI^{2}=GH^{2}\), triangle \(GHI\) is a right - triangle.

Step5: Check option D

\(JK = 10\), \(KL = 13\), \(JL = 17\).
\(JK^{2}+KL^{2}=10^{2}+13^{2}=100 + 169=269\), \(JL^{2}=17^{2}=289\).
Since \(269
eq289\), triangle \(JKL\) is not a right - triangle.

Answer:

C. Triangle \(GHI\) with \(GI = 9\), \(HI = 12\), and \(GH = 15\)