Q1 of 49 Page 58

Suppose ABCD is a rectangle. Using the RHS theorem, prove that triangles ABC and ADC are congruent.

Capture.JPG


ABCD is a rectangle


AC is a diagonal


In Δ ABC and Δ ADC


AD = BC (Opposite sides of a rectangle)


∠ADC = ∠ABC = 900(Angle of a rectangle)


AC = AC (Common side)


So Δ ABC and Δ ADC is congruent by R.H.S. axiom of congruency.


More from this chapter

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3

In the figure, two sides AB, BC and the median AD of ΔABC are respectively equal to two sides PQ, QR and median PS of ΔPQR. Prove that

(i) ΔADB ≅ ΔPSQ;


(ii) ΔADC ≅ ΔPSR.


Does it follow that triangles ABC and PQR are congruent?


 4

In ΔPQR, PQ = QR; L, M, and N are the midpoints of the sides of PQ, QR and RP respectively. Prove that LN = MN.

 2

Suppose ABC is a triangle and D is the midpoint of BC. Assume that the perpendiculars from D to AB and AC are of equal length. Prove that ABC is isosceles.

 3

Suppose ABC is a triangle in which BE and CF are respectively the perpendiculars to the sides AC and AB. If BE = CF, prove that triangle ABC is isosceles.