Maths Pythagoras Theorem Chapter Test

Pythagoras Theorem Chapter Test

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Q1 (a) In fig. (i) given below, AD ⊥ BC, AB = 25 cm, AC = 17 cm and AD = 15 cm. Find the length of BC.

(b) In figure (ii) given below, ∠BAC = 90°, ∠ADC = 90°, AD = 6 cm, CD = 8 cm and BC = 26 cm. Find :

(i) AC
(ii) AB
(iii) area of the shaded region.

(c) In figure (iii) given below, triangle ABC is right angled at B. Given that AB = 9 cm, AC = 15 cm and D, E are mid-points of the sides AB and AC respectively, calculate

(i) the length of BC (ii) the area of ∆ADE.

Q2 If in ∆ ABC, AB > AC and AD ⊥ BC, prove that AB² - AC² = BD² - CD².

Q3 In a right angled triangle ABC, right angled at C, P and Q are the points on the sides CA and CB respectively which divide these sides in the ratio 2 : 1. Prove that

(i) 9AQ² = 9AC² + 4BC²
(ii) 9BP² = 9BC² + 4AC²
(iii) 9(AQ² + BP²) = 13AB².

Q4 In the given figure, ∆PQR is right angled at Q and points S and T trisect side QR. Prove that 8PT² = 3PR² + 5PS².

Q5 In a quadrilateral ABCD, ∠B = 90°. If AD² = AB² + BC² + CD², prove that ∠ACD = 90°.

Q6 In the given figure, find the length of AD in terms of b and c.

Q7 ABCD is a square, F is mid-point of AB and BE is one-third of BC. If area of ∆FBE is 108 cm2, find the length of AC.

Q8 In a triangle ABC, AB = AC and D is a point on side AC such that BC² = AC x CD. Prove that BD = BC.

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