Q3 of 49 Page 51

In the figure, AP and BQ are perpendiculars to the line segment AB and AP = BQ. Prove that O is the midpoint of line segment AB as well as PQ.

In Δ AOP and Δ BOQ


AP = BQ (Given)


∠AOP = ∠BOQ (Vertically Opposite)


∠PAO = ∠OBO (Perpendiculars)


So AOP and Δ BOQ are congruent to each other by A.A.S. axiom of congruency


Hence we can say


AO = OB(Corresponding parts of Congruent triangles)


PO = OQ(Corresponding parts of Congruent triangles)


More from this chapter

All 49 →
1

In the given figure, If AB || DC and P is the midpoint of BD, prove that P is also the midpoint of AC.

 2

In the adjacent figure, CD and BE are altitudes of an isosceles triangle ABC with AC = AB. Prove that AE = AD.

 4

Suppose ABC is an isosceles triangle with AB = AC; BD and CE are bisectors of ∠B and ∠C. Prove that BD = CE.

 5

Suppose ABC is an equiangular triangle. Prove that it is equilateral.(You have seen earlier that an equilateral triangle is equiangular. Thus for triangles equiangularity is equivalent to equilaterality.)