In a triangle ABC, D is the mid-point of side AC such that BD = 1/2 AC. Show that ∠ABC is a right angle.

Question

TextCongruence of TrianglesNCERT Exemplar

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Which of the following is not a criterion for congruence of triangles?

Congruence of Triangles

SAS Congruence Rule for Triangles

ASA Congruence Rule for Triangles

SSS Congruence Rule for Triangles

ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.

If ∆ ABC ≅ ∆ PQR and ∆ ABC is not congruent to ∆ RPQ, then which of the following is not true:

ABC is an isosceles triangle with AB = AC and BD and CE are its two medians. Show that BD = CE.

In Fig.7.4, D and E are points on side BC of a ∆ ABC such that BD = CE and AD = AE. Show that ∆ ABD ≅ ∆ ACE.

In Fig. 7.9, ABC is a right triangle and right angled at B such that ∠BCA = 2 ∠BAC. Show that hypotenuse AC = 2 BC.