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For finding AB and BC with the help of information given in figure 2.20, complete following activity. (In ΔABC, ∠B = 90°, AB = BC, AC = √8)

For finding AB and BC with the help of information given in figure 2.20, complete following activity.

Figure: In \(\triangle ABC\), \(\angle ABC = 90^\circ\), AB = BC and AC = \(\sqrt{8}\).

AB = BC ………. □

\(\therefore \angle BAC\) = □

\(\therefore\) AB = BC = □ × AC = □ × \(\sqrt{8}\) = □ × \(2\sqrt{2}\) = □

1 answer

Answer: AB = BC = 2

AB = BC …… given

So \(\triangle ABC\) is an isosceles right-angled triangle and \(\angle BAC = \angle BCA = 45^\circ\).

In a \(45^\circ\)–\(45^\circ\)–\(90^\circ\) triangle, each side forming the right angle is \(\frac{1}{\sqrt{2}}\) × hypotenuse:

\[AB = BC = \frac{1}{\sqrt{2}} \times \sqrt{8}\] \[= \frac{1}{\sqrt{2}} \times 2\sqrt{2} = 2\]

Blanks: Given; \(45^\circ\); \(\frac{1}{\sqrt{2}}\); \(\frac{1}{\sqrt{2}}\); \(\frac{1}{\sqrt{2}}\); 2.

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report
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