### Practice Set 2.2 Pythagoras Theorem Class 10th Mathematics Part 2 MHB Solution

Practice Set 2.2

1. In ΔPQR, point S is the midpoint of side QR. If PQ = 11,PR = 17, PS = 13,find QR.…
2. In ΔABC, AB = 10, AC = 7, BC = 9 then find the length of the median drawn from point C…
3. In the figure 2.28 seg PS is themedian of ΔPQR and PT ⊥ QR. Prove that, (1) pr^2 = ps^2…
4. In ΔABC, point M is the midpointof side BC. If, AB^2 + AC^2 = 290 cm^2 ,AM = 8 cm, find…
5. In figure 2.30, point T is in theinterior of rectangle PQRS, Prove that, TS^2 + TQ^2 =…

###### Practice Set 2.2
Question 1.

In ΔPQR, point S is the midpoint of side QR. If PQ = 11,PR = 17, PS = 13,find QR. Given PS = 13, PQ = 11,PR = 17

By Apollonius's Theorem,

PS2 = ⇒ 169 = ⇒ = 36

⇒ QR2 = 144

QR = 12

Question 2.

In ΔABC, AB = 10, AC = 7, BC = 9 then find the length of the median drawn from point C to side AB

The figure is given below: According to Pythagoras theorem,

Median2 = ⇒ Median2 = ⇒ Median2 = 40

Median = 2√10

Thus the median is 2√10

Question 3.

In the figure 2.28 seg PS is the median of ΔPQR and PT ⊥ QR. Prove that,
(1) (2)  Answer: (i) In ΔPTR, PT ⊥ TR, By Pythagoras Theorem we have

Perpendicular2 + Base2 = Hypotenuse2

⇒ PT2 + TR2 = PR2 

Similarly, In ΔPTS

PT2 + TS2 = PS2

⇒ PT2 = PS2 – ST

Using  in , we have

⇒ PS2 – ST2 + (ST + SR)2 = PR2

⇒ PS2 – ST2 + ST2 + SR2 + (2 × ST × SR) = PR2

Now, Since PS is a median we can write (ii)

In ΔPQT, By Pythagoras we have

PQ2 = PT2 + QT2

⇒ PQ2 = PS2 – ST2 + (QS – ST)2 [From 2]

⇒ PQ2 = PS2 – ST2 + QS2 + ST2 – (2 × QS × ST) Question 4.

In ΔABC, point M is the midpointof side BC.

If, AB2 + AC2 = 290 cm2,AM = 8 cm, find BC. Given AB2 + AC2 = 290 cm2,AM = 8 cm, BM = MC

According to formula,

AM2 = ⇒ 64 = ⇒ 64 – ⇒ BC2 = 324

BC = 18.

Thus BC = 18 cm.

Question 5.

In figure 2.30, point T is in theinterior of rectangle PQRS, Prove that, TS2 + TQ2 = TP2 + TR2(As shown in the figure, drawseg AB || side SR and A – T – B) From figure,

In ∆PAT, ∠PAT = 900

TP2 = AT2 + PA2 …1

In ∆AST, ∠SAT = 900

TS2 = AT2 + SA2 …2

In ∆QBT, ∠QBT = 900

TQ2 = BT2 + QB2 …3

In ∆BTR, ∠RBT = 900

TR2 = BT2 + BR2 …4

TS2 + TQ2 = AT2 + SA2 + BT2 + QB2 [Adding 2 and 3]

⇒ TS2 + TQ2 = AT2 + PA2 + BT2 + BR2 [SA = BR, QB = AP]

⇒ TS2 + TQ2 = TP2 + TR2 [From 1 and 4]

PROVED.

PDF FILE TO YOUR EMAIL IMMEDIATELY PURCHASE NOTES & PAPER SOLUTION. @ Rs. 50/- each (GST extra)

HINDI ENTIRE PAPER SOLUTION

MARATHI PAPER SOLUTION

SSC MATHS I PAPER SOLUTION

SSC MATHS II PAPER SOLUTION

SSC SCIENCE I PAPER SOLUTION

SSC SCIENCE II PAPER SOLUTION

SSC ENGLISH PAPER SOLUTION

SSC & HSC ENGLISH WRITING SKILL

HSC ACCOUNTS NOTES

HSC OCM NOTES

HSC ECONOMICS NOTES

HSC SECRETARIAL PRACTICE NOTES

# 2019 Board Paper Solution

HSC ENGLISH SET A 2019 21st February, 2019

HSC ENGLISH SET B 2019 21st February, 2019

HSC ENGLISH SET C 2019 21st February, 2019

HSC ENGLISH SET D 2019 21st February, 2019

SECRETARIAL PRACTICE (S.P) 2019 25th February, 2019

HSC XII PHYSICS 2019 25th February, 2019

CHEMISTRY XII HSC SOLUTION 27th, February, 2019

OCM PAPER SOLUTION 2019 27th, February, 2019

HSC MATHS PAPER SOLUTION COMMERCE, 2nd March, 2019

HSC MATHS PAPER SOLUTION SCIENCE 2nd, March, 2019

SSC ENGLISH STD 10 5TH MARCH, 2019.

HSC XII ACCOUNTS 2019 6th March, 2019

HSC XII BIOLOGY 2019 6TH March, 2019

HSC XII ECONOMICS 9Th March 2019

SSC Maths I March 2019 Solution 10th Standard11th, March, 2019

SSC MATHS II MARCH 2019 SOLUTION 10TH STD.13th March, 2019

SSC SCIENCE I MARCH 2019 SOLUTION 10TH STD. 15th March, 2019.

SSC SCIENCE II MARCH 2019 SOLUTION 10TH STD. 18th March, 2019.

SSC SOCIAL SCIENCE I MARCH 2019 SOLUTION20th March, 2019

SSC SOCIAL SCIENCE II MARCH 2019 SOLUTION, 22nd March, 2019

XII CBSE - BOARD - MARCH - 2019 ENGLISH - QP + SOLUTIONS, 2nd March, 2019

# HSCMaharashtraBoardPapers2020

(Std 12th English Medium)

HSC ECONOMICS MARCH 2020

HSC OCM MARCH 2020

HSC ACCOUNTS MARCH 2020

HSC S.P. MARCH 2020

HSC ENGLISH MARCH 2020

HSC HINDI MARCH 2020

HSC MARATHI MARCH 2020

HSC MATHS MARCH 2020

# SSCMaharashtraBoardPapers2020

(Std 10th English Medium)

English MARCH 2020

HindI MARCH 2020

Hindi (Composite) MARCH 2020

Marathi MARCH 2020

Mathematics (Paper 1) MARCH 2020

Mathematics (Paper 2) MARCH 2020

Sanskrit MARCH 2020

Sanskrit (Composite) MARCH 2020

Science (Paper 1) MARCH 2020

Science (Paper 2)

Geography Model Set 1 2020-2021

MUST REMEMBER THINGS on the day of Exam

Are you prepared? for English Grammar in Board Exam.

Paper Presentation In Board Exam

How to Score Good Marks in SSC Board Exams

Tips To Score More Than 90% Marks In 12th Board Exam

How to write English exams?

How to prepare for board exam when less time is left

How to memorise what you learn for board exam

No. 1 Simple Hack, you can try out, in preparing for Board Exam

How to Study for CBSE Class 10 Board Exams Subject Wise Tips?

JEE Main 2020 Registration Process – Exam Pattern & Important Dates

NEET UG 2020 Registration Process Exam Pattern & Important Dates

How can One Prepare for two Competitive Exams at the same time?

8 Proven Tips to Handle Anxiety before Exams!