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The three angles of triangle A have measures 90, x and y degrees and
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28 Feb 2025, 00:49
28 Feb 2025, 00:49
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The three angles of triangle A have measures 90, x and y degrees and the angles of triangle B have measures of 90, z and w degrees. Which of the following conditions must be true for the two triangles?
I. x – w = z – y
II. x + y = w
III. z = 90 – w
A. I only
B. II only
C. I and III
D. II and III
E. I, II and III
I. x – w = z – y
II. x + y = w
III. z = 90 – w
A. I only
B. II only
C. I and III
D. II and III
E. I, II and III
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Re: The three angles of triangle A have measures 90, x and y degrees and
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28 Feb 2025, 02:55
28 Feb 2025, 02:55
Carcass
how come it's option C. It's clearly mentioned that which of the following are true for "two triangles"
z = 90 - w is true only for one triangle and that is triangle B
how come it's option C. It's clearly mentioned that which of the following are true for "two triangles"
z = 90 - w is true only for one triangle and that is triangle B
Re: The three angles of triangle A have measures 90, x and y degrees and
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28 Feb 2025, 09:33
28 Feb 2025, 09:33
Expert Reply
The three angles of triangle A have measures $\(90, x\)$ and $\(y\)$, so we get $\(90+x+y=180\)$ which gives $\(x+y=90\)$. $\(\qquad\)$
Also the three angles of triangle $B$ have measures 90 , $\(z\)$ and $\(w\)$, so we get $\(90+z+w=180\)$, which gives $\(\mathrm{z}+\mathrm{w}=90\)$. $\(\qquad\)$
Now, checking from the statements we have
I. $\(x-w=z-y\)$ i.e. $\(x+y=z+w\)$, which is true using (1) \& (2).
II. $\(x+y=w\)$, which cannot be true as we have $\(x+y=w+z\)$
III. $\(z=90-w\)$ i.e. $\(z+w=90\)$, which is true using (2).
Hence statements \(I \& III \)are true, so the answer is (C).
Also the three angles of triangle $B$ have measures 90 , $\(z\)$ and $\(w\)$, so we get $\(90+z+w=180\)$, which gives $\(\mathrm{z}+\mathrm{w}=90\)$. $\(\qquad\)$
Now, checking from the statements we have
I. $\(x-w=z-y\)$ i.e. $\(x+y=z+w\)$, which is true using (1) \& (2).
II. $\(x+y=w\)$, which cannot be true as we have $\(x+y=w+z\)$
III. $\(z=90-w\)$ i.e. $\(z+w=90\)$, which is true using (2).
Hence statements \(I \& III \)are true, so the answer is (C).
