Question

Can anyone help me to get case based questions on Class 9 Maths Ch-7 Triangles. CBSE ​

Answer 1

Answer:

Important Questions & Solutions For CBSE Class 9 Chapter 7 (Triangles)

Q.1: ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA. Prove that

(i) ΔABD ≅ ΔBAC

(ii) BD = AC

(iii) ∠ABD = ∠BAC.

class 9 maths chapter 7 imp.ques.1

Solution:

As per given in the question,

∠DAB = ∠CBA and AD = BC.

(i) ΔABD and ΔBAC are similar by SAS congruency as

AB = BA (common arm)

∠DAB = ∠CBA and AD = BC (given)

So, triangles ABD and BAC are similar

i.e. ΔABD ≅ ΔBAC. (Hence proved).

(ii) As it is already proved,

ΔABD ≅ ΔBAC

So,

BD = AC (by CPCT)

(iii) Since ΔABD ≅ ΔBAC

So, the angles,

∠ABD = ∠BAC (by CPCT).

Q.2: AD and BC are equal perpendiculars to a line segment AB. Show that CD bisects AB.

class 9 maths chapter 7 imp.ques.2

Solution:

Given, AD and BC are two equal perpendiculars to AB.

To prove: CD is the bisector of AB

Proof:

Triangles ΔAOD and ΔBOC are similar by AAS congruency

Since:

(i) ∠A = ∠B (perpendicular angles)

(ii) AD = BC (given)

(iii) ∠AOD = ∠BOC (vertically opposite angles)

∴ ΔAOD ≅ ΔBOC.

So, AO = OB ( by CPCT).

Thus, CD bisects AB (Hence proved)

Step-by-step explanation:

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