## 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
Solution 10
Question 11
Solution 11
Question 12
Solution 12
Question 13
Solution 13
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
Solution 23
Question 24
Solution 24
Question 25
Solution 25
Question 26
Solution 26