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.
Chapter 17 - Pythagoras Theorem Exercise Ex. 17.1
InABC, AD is perpendicular to BC. Prove that
AB2 + CD2 = AC2 + BD2
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
In a triangle ABC, AC > AB, D is the midpoint BC, and AEBC. Prove that:
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.
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.
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.
PQR is an isosceles triangle with PQ = PR = 10 cm and QR = 12 cm. Find the length of the perpendicular from P to QR.
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.
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