Angle HAB = 72° B F I 72˚ (a) What is the size of angle CBI? (b) The bar BH bisects the angle ABI. (i) (c) 2. G H A (1 mark) What is the size of angle IBH? (1 mark) What is the size of angle FHG? (1 mark) Name a triangle which is congruent to triangle CBI. (1 mark) The sloping sides of a flower bowl are part of a cone as shown. The radius of the top of the bowl is 10 cm and the radius of the bottom of the bowl is 5 cm. The height of the full cone is 24 cm. Not to scale 10 cm
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4. If the base of an isosceles triangles are produced both ways‚ show that the exterior angles so formed are equal. 5. In the figure‚ AD= AE‚ BD= CE and ∠AEC=∠ADB. Prove that AB = AC. 6. In the figure‚ ΔABC and ΔDBC are both isosceles triangles. Prove that‚ ΔABD = ACD. 7. Show that the medians drawn from the extremities of the base of an isosceles triangle to the opposite sides are equal to one another. 8. Prove that the angles of an equilateral triangle are equal to one another. 10.2
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5C Problems involving triangles cQ1. The diagram shows a sector AOB of a circle of radius 15 cm and centre O. The angle at the centre of the circle is 115. Calculate (a) the area of the sector AOB. (b) the area of the shaded region. (226 ‚ 124 nQ2. Consider a triangle and two arcs of circles. The triangle ABC is a right-angled isosceles triangle‚ with AB = AC = 2. The point P is the midpoint of [BC]. The arc BDC is part of a circle with centre A
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Surface area of sphere = 4ʌU 2 1 2 ʌU h 3 Curved surface area of cone = ʌUO r l h r The Quadratic Equation The solutions of ax2 + bx + c = 0 where D0‚ are given by In any triangle ABC C b A Sine Rule a x= B c −b ± (b 2 − 4ac) 2a a b c = = sin A sin B sin C Cosine Rule a2 = b2 + c 2 – 2bc cos A Area of triangle = 2 1 ab
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information to be manipulated too create two isosceles triangles. The first triangle and the one that is given‚ ∆OPA is an isosceles triangle therefore it can be concluded‚ thanks to the Isosceles Triangle Theorem that angle O and A are congruent to each other in this triangle. ∆OPA is not the only triangle that can be created‚ ∆OP’A is the second triangle created with a radius from C2. Therefore ∆OP’A is also an isosceles triangle. Now in both the triangles stated above‚ they share a common angle‚ O. With
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3 A tent has a groundsheet as its horizontal base. The shape of the tent is a triangular prism of length 8 metres‚ with two identical half right-circular cones‚ one at each end. The vertical cross-section of the prism is an isosceles triangle of height 2.4 metres and base 3.6 metres. (a) Calculate the area of the groundsheet. Give
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Q: 6 Under which of the following conditions are you most likely to fall sick? (a) When you are taking examinations. (b) When you have travelled by bus and train for two days. (c) When your friend is suffering from measles. Why? Answer I will be most likely to fall sick when my friend is suffering from measles. This is because in this condition‚ I will visit my friend and will be likely to get infected with measles. Measeles is an infectious as well as an air-borne disease. When
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14/09/2013 Important Formulae_for website_for CAT2012 students RATIO – PROPORTION – VARIATION 1. If a : b : : c : d‚ then ad = bc 2. If a : b : : c : d‚ then a + b : b : : c + d : d 3. If a : b : : c : d‚ then a - b : b : : c - d : d 4. If a : b : : c : d‚ then a + b : a - b : : c + d : c - d 5. If then k = NUMBERS 1. a 3 + b 3 + c3 – 3abc = (a + b + c) (a 2 + b 2 + c2 – ab – bc – ca) 2. The product of n consecutive integers is always divisible by n! (n factorial) 3. The sum
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polynomial is : 4. The remainder when a. 1 b. c. d. is divided by is 5. Two sides of a triangle are of lengths 7 cm and 3.5 cm. The length of the 3rd side cannot be a. 4.1 cm b. 3.4 cm c. 3.8 cm d. 3.6 cm Copyright © 2013 Learnhive Education Pvt. Ltd. Learnhive Education Pvt. Ltd. www.learnhive.com 6. If one angle of a triangle is equal to the sum of other two angles‚ then the triangle is a. Obtuse b. Equilateral c. Isosceles d. Right 7. the angle POB equals a. b. c. d. 54 48
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prayed Verdant Green with vegetation; covered with green plants. When the trees are still verdant‚ we promise to go to a trip. Vertex The point opposite and farthest from the base; summit. It was as acute as the vertex of an isosceles triangle
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