In this chapter, we provide RD Sharma Solutions for Chapter 12 Heron’s Formula Ex 12.4 for English medium students, Which will very helpful for every student in their exams. Students can download the latest RD Sharma Solutions for Chapter 12 Heron’s Formula Ex 12.4 Maths pdf, free RD Sharma Solutions for Chapter 12 Heron’s Formula Ex 12.4 Maths book pdf download. Now you will get step by step solution to each question.

Textbook | NCERT |

Class | Class 9 |

Subject | Maths |

Chapter | Chapter 12 |

Chapter Name | Heron’s Formula |

Exercise | Ex 12.4 |

**RD Sharma Solutions for Class 9 Chapter 12 Heron’s Formula Ex 12.4 Download PDF**

Question 1.

In the figure, it is given that AB = CD and AD = BC. Prove that ∆ADC ≅ ∆CBA.

RD Sharma Class 9 Solutions Chapter 12 Heron’s Formula Ex 12.4 – 1

Solution:

Given : In the figure, AB = CD, AD = BC

RD Sharma Class 9 Solutions Chapter 12 Heron’s Formula Ex 12.4 – 2

To prove : ∆ADC = ∆CBA

Proof : In ∆ADC and ∆CBA

CD = AB (Given)

AD = BC (Given)

CA = CA (Common)

∴ ∆ADC ≅ ∆CBA (SSS axiom)

Question 2.

In a APQR, if PQ = QR and L, M and N are the mid-points of the sides PQ, QR and RP respectively. Prove that LN = MN.

Solution:

Given : In ∆PQR, PQ = QR

L, M and N are the mid-points of sides PQ, QR and RP respectively. Join LM, MN and LN

RD Sharma Class 9 Solutions Chapter 12 Heron’s Formula Ex 12.4 – 2A

To prove : ∠PNM = ∠PLM

Proof : In ∆PQR,

∵ M and N are the mid points of sides PR and QR respectively

∴ MN || PQ and MN = 12 PQ …(i)

∴ MN = PL

Similarly, we can prove that

LM = PN

Now in ∆NML and ∆LPN

MN = PL (Proved)

LM = PN (Proved)

LN = LN (Common)

∴ ∆NML = ∆LPN (SSS axiom)

∴ ∠MNL = ∠PLN (c.p.c.t.)

and ∠MLN = ∠LNP (c.p.c.t.)

⇒ ∠MNL = ∠LNP = ∠PLM = ∠MLN

⇒ ∠PNM = ∠PLM

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