FRANK Solutions for Class 9 Maths Chapter 17 - Pythagoras Theorem

Chapter 17 - Pythagoras Theorem Exercise Ex. 17.1

Question 1

InABC, AD is perpendicular to BC. Prove that

AB² + CD² = AC² + BD²

Solution 1

Question 2

From a point O in the interior of aABC, 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 2

Question 3

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

 

Solution 3

Question 4

 

Solution 4

Question 5

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 5

Question 6

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 6

Question 7

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 7

Question 8

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 8

Question 9

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 9

Question 10

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Question 11

Solution 11

Question 12

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Question 13

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Question 14

Solution 14

Question 15

 

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

Solution 22

Question 23

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Question 24

Solution 24

Question 25

Solution 25

Question 26

Solution 26