Prove that in a triangle, other than an equilateral triangle, angle opposite the longest side is greater than 2/3 of a right angle.

Question

TextRelationship Between Sides and Opposite Angles in TriangleNCERT Exemplar

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D is a point on the side BC of a ∆ ABC such that AD bisects ∠BAC. Then

In ∆ PQR, if ∠R > ∠Q, then

In ∆ PQR, ∠P = 70° and ∠R = 30°. Which side of this triangle is the longest? Give reason for your answer.

In Fig.7.3, PQ > PR and QS and RS are the bisectors of ∠Q and ∠R, respectively. Show that SQ > SR.

Q is a point on the side SR of a ∆ PSR such that PQ = PR. Prove that PS > PQ.

D is any point on side AC of a ∆ ABC with AB = AC. Show that CD < BD.