Q26 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)

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.

According to the question,

AB = AC

∠ACB = ∠ABC (i)

Now, ∠ACD >∠ACB =∠ABC (Side BC is produced to D)

And, In ∆ADC, side DC is produced to B

∠ACB>∠ADC (ii)

∠ABC>∠ADC

Now, using (i) and (ii),

AD >AB

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

∴ Option C is correct

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)
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.

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)-……..,

Fill in the blanks with < or >.

(A) (Sum of any two sides of a triangle)………… (the third side)

(B) (Difference of any two sides of a triangle)………… (the third side)

(D) (Sum of any two sides of a triangle)…….. (twice the median to the 3^rd side)

(E) (Perimeter of a triangle)…………. (Sum of its three medians)