Chapter 17 : Pythagoras Theorem - Frank Solutions for Class 9 Maths ICSE

Mathematics in ICSE Class 9 is one of the most challenging and trickiest subjects of all. It includes complex topics such as logarithms, expansions, indices and Pythagoras Theorem which are difficult to understand for an average student. TopperLearning provides study materials for ICSE Class 9 Mathematics to make the subject easy and help students to clear all their concepts. Our study materials comprise numerous video lessons, question banks, revision notes and sample papers which help achieve success in the examination.

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Chapter 17 - Pythagoras Theorem Exercise Ex. 17.1

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

 

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

In ABC, AD is perpendicular to BC. Prove that

AB2 + CD2 = AC2 + BD2

Solution 12

Question 13

Solution 13

Question 14

From a point O in the interior of a ABC, perpendicular OD, OE and OF are drawn to the sides BC, CA and AB respectively. Prove that:

a. AF2 + BD2 + CE2 = OA2 + OB2 + OC2 - OD2 - OE2 - OF2

b. AF2 + BD2 + CE2 = AE2 + CD2 + BF2

Solution 14

 

 

Question 15

In a triangle ABC, AC > AB, D is the midpoint BC, and AE BC. Prove that:

  

Solution 15

 

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

  

 

Solution 21

Question 22

Ina right-angled triangle ABC, ABC = 90°, AC = 10 cm, BC = 6 cm and BC produced to D such CD = 9 cm. Find the length of AD.

Solution 22

 

Question 23

In the given figure. PQ = PS,  P = R = 90°. RS = 20 cm and QR = 21 cm. Find the length of PQ correct to two decimal places.

Solution 23

Question 24

In a right-angled triangle PQR, right-angled at Q, S and T are points on PQ and QR respectively such as PT = SR = 13 cm, QT = 5 cm and PS = TR. Find the length of PQ and PS.

Solution 24

Question 25

PQR is an isosceles triangle with PQ = PR = 10 cm and QR = 12 cm. Find the length of the perpendicular from P to QR.

Solution 25

Question 26

In a square PQRS of side 5 cm, A, B, C and D are points on sides PQ, QR, RS and SP respectively such as PA = PD = RB = RC = 2 cm. Prove that ABCD is a rectangle. Also, find the area and perimeter of the rectangle.

Solution 26

 

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