The angle ABC = 56^o as it is in the alternate segment to the angle CAE. Here, angle ABC is incorrectly calculated as 180 - 56 = 124^o. The angle is taken from 180^o which is a confusion with opposite angles in a cyclic quadrilateral. Opposite angles in a cyclic quadrilateral.Top tip: Use arrows to visualise which way the alternate segment angle appears: The chord BC is assumed to be parallel to the tangent and so the angle ABC is equal to the angle at the tangent. Parallel lines (alternate segment theorem).The angle at the circumference is assumed to be 90^o when the associated chord does not intersect the centre of the circle and so the diagram does not show a semicircle. They should total 90^o as the angle in a semicircle is 90^o. The angles that are either end of the diameter total 180^o as if the triangle were a cyclic quadrilateral. Look out for isosceles triangles and the angles in the same segment. Make sure that you know when two angles are equal. The angle at the centre is always larger than the angle at the circumference (this isn’t so obvious when the angle at the circumference is in the opposite segment). Make sure you know the other angle facts including:īy remembering the angle at the centre theorem incorrectly, the student will double the angle at the centre, or half the angle at the circumference. To Construct a Triangle whose Three Sides are given.Below are some of the common misconceptions for all of the circle theorems: (vi) A triangle with unequal sides is called a ……………………… (v) A triangle whose 2 sides are equal is called a ……………………… (iv) A triangle with all sides equal is called a ……………………… (iii) A triangle can be classified on the basis of ……………………… (i) A triangle is ……………………… sided polygon. (e) A triangle can have two obtuse angles. (d) Equiangular triangle has its three sides also equal. (b) If one angle of a triangle is obtuse, the other two angles must be acute. (a) All the angles of an isosceles triangle are equal. Find the other acute angle.ġ6. Say whether the following statements are true or false: What kind of triangle is this?ġ5. One of the acute angles of a right triangle is 48°. Find the length of its third side.ġ4. Each side of a ∆ is one third of its perimeter. Determine the other angles.ġ3. The perimeter of a triangle is 24 cm. Find the measure of each angle of the triangle.ġ2. One of the two equal angles of an isosceles triangle measures 55°. Measure its sides andĬlassify the triangle as Isosceles triangle, scalene triangle or equilateralġ1. The angle of a triangle is in the ratio of 2: 3: 4. (e) 50°, 50°, 90° (f) 10 cm, 12 cm, 2 cm.Ĩ. Find the perimeter of a triangle when its sides are: (f) 3.5 cm, 3.5 cm, 4.5 cm.ħ. Is it possible to have a triangle with the following angles and sides? Give reason in support of your answer. Classify the triangle according to sides, that is, equilateral, isosceles and scalene triangles
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