Question

the two triangles shown in the figure are similar.
which statement is not correct?
m + n + s = 180°
m + n = q + r
n = q + s
n = 180° - q - s

Explanation:

Step1: Use the property of similar triangles

Since the two triangles are similar, \(m = s\) and \(p = q\).

Step2: Use the angle - sum property of a triangle

For the first triangle, \(m + n + p=180^{\circ}\). Substitute \(p = q\) and \(m = s\), we get \(s + n+q = 180^{\circ}\), so \(n=180^{\circ}-q - s\).

Step3: Analyze each option

• Option 1: \(m + n + s\). Since \(m = s\), \(m + n + s=2s + n

eq180^{\circ}\) (because \(s + n+q = 180^{\circ}\) and \(q
eq s\) in general).

• Option 2: For the first triangle, \(m + n=180^{\circ}-p\). For the second triangle, \(q + r=180^{\circ}-s\). Since \(m = s\) and \(p = q\), \(180^{\circ}-p = 180^{\circ}-q\) and \(180^{\circ}-s=180^{\circ}-m\), so \(m + n=q + r\).
• Option 3: \(n = 180^{\circ}-q - s\) (from angle - sum property of the second triangle).
• Option 4: \(n = 180^{\circ}-q - s\) (already derived from the angle - sum property of the second triangle).

Answer:

\(m + n + s = 180^{\circ}\)