Q25 of 97 Page 195

The question consists of two statements, namely, Assertion (A) and Reason (R). Please select the correct answer.

Assertion (A)

Reason (R)

It is always possible to draw a triangle whose sides measure 4 cm, 5cmand 10cm respectively.

In an isosceles ∆ABC with AB=AC, if BD and CE are bisectors of ∠B and ∠C respectively, then BD=CE.

In ΔBDC and ΔCEB,

∠DCB = ∠EBC (Given)

BC = CB (Common)

∠B = ∠C (AC = AB)

∠CEB = ∠BCE

∴ ΔBDC ≅ ΔCEB

BD = CE (By c.p.c.t.)

And, we know that the sum of two sides is always greater than the third side in any triangle.

But, (5 + 4) < 10

Hence, the reason is true, but the assertion is false.

∴ Option D is true

The question consists of two statements, namely, Assertion (A) and Reason (R). Please select the correct answer.

Assertion (A)

Reason (R)

In a quadrilateral ABCD, we have (AB+BC+CD+DA)>2AC.

The sum of any two sides of a triangle is greater than the third side.

The question consists of two statements, namely, Assertion (A) and Reason (R). Please select the correct answer.

Assertion (A)

Reason (R)

∆ABC and ∆DBC are two isosceles triangles on the same base BC. Then, ∠ABD=∠ACD.

The angles opposite to equal sides of a triangle are equal.

The question consists of two statements, namely, Assertion (A) and Reason (R). Please select the correct answer.

Assertion (A)

Reason (R)

In the given figure, ∆ABC is given with AB=AC and BA is produced to D, such that AB=AD.

Then, ∠BCD=90°.

In the given figure AB=AC and D is a point on BC produced. Then, AB>AD.

Match the following columns.

Column I	Column II
(a)In ∆ABC, if AB=AC and ∠A=50°, then ∠C=…………….	(p) its perimeter
(b) The vertical angle of an isosceles triangle is 130°. Then, each base angle is…….	(q) 15°
(c) The sum of three altitudes of a ∆ABC is less than…………	(r) 65°
(d) In the given figure, ABCD is a square and ∆EDC is an equilateral triangle. Then, ∠EBC is………….	(s) 25°

The correct answer is:

(A)-………, (B)-………, (C)-…….., (D)-……..,

Assertion (A)	Reason (R)
It is always possible to draw a triangle whose sides measure 4 cm, 5cmand 10cm respectively.	In an isosceles ∆ABC with AB=AC, if BD and CE are bisectors of ∠B and ∠C respectively, then BD=CE.