Q4 of 49 Page 61

Let ABCD be a quadrilateral in which AD is the largest side and BC is the smallest side. Prove that ∠A <∠C. (Hint: Join AC)

Capture.JPG


ABCD is a quadrilateral with AD being the largest and BC being the smallest side


AC is a diagonal of the quadrilateral


Applying the law of Inequality of triangle in Δ BAC


∠BAC < ∠BCA (BC is the shortest side) …(i)


Applying the law of Inequality of triangle in Δ ACD


∠CAD < ∠DCA (AD is the largest side) …(ii)


Adding (i) and (ii) we get


∠BAC + ∠CAD < ∠BCA + ∠DCA


⇒ ∠A < ∠C


Hence Proved


More from this chapter

All 49 →
2

In a triangle ABC, we have AB = 4cm, BC = 5.6cm and CA = 7.6cm. Write the angles of the triangle in ascending order of measures.

 3

Let ABC be a triangle such that ∠B = 70° and ∠C = 40°. Suppose D is a point on BC such that AB = AD. Prove that AB > CD.

 5

Let ABC be a triangle and P be an interior point. Prove that AB + BC + CA < 2 (PA + PB + PC).

 1

Fill in the blanks to make the statements true.

(a) In right triangle the hypotenuse is the ______ side.


(b) The sum of three altitudes of a triangle is ______ than its perimeter.


(c) The sum of any two sides of a triangle is ______ than the third side.


(d) If two angles of a triangle are unequal, then the smaller angle has the ______ side opposite to it.


(e) Difference of any two sides of a triangle is ______ than the third side.


(f) If two sides of a triangle are unequal, then the larger side has ______ angle opposite to it.