## Chapter 17 - Pythagoras Theorem Exercise Ex. 17.1

Question 1
In ABC, AD is perpendicular to BC. Prove that
AB2 + CD2 = AC2 + BD2
Solution 1  Question 2
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 2  Question 3
In a triangle ABC, AC > AB, D is the midpoint BC, and AE BC. 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 