# 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  