Grade 11 Euclidean Geometry, Exercises of Mathematics

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EUCLIDEAN

GEOMETRY

GRADE 11

PART ONE

THE BASICS

Vertically opposite angles are equal

Angles on a straight line add up to 𝟏𝟖𝟎°

Corresponding Angles ❑ Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line (i.e. the transversal)

Alternate angles ❑ These are angles that occur on opposite sides of the transversal line and have the same size. ❑ Alternate angles are equal :

Properties of triangles

Pythagoras Theorem ❖ The Pythagoras theorem explains the relationship between the three sides of a right-angled triangle. ❖ According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

Parts of a circle

THE THEOREMS

Practice Questions on Theorem 1 Question 1 In the diagram below, O is the center. OB = 3 cm, AC = 8 cm and OB ⊥ AC. Calculate the length a) AB b) OC

Question 2 In the diagram below ,O is the centre. AC = 16 units, AB = BC and AO = 17 units Calculate the length of OB.

Subtended Angle ❑ A subtended angle is the angle between two lines at a point. For example in the triangle below, the side AC subtends the angle θ ❖ For circle theorems, a subtended angle is an angle within a circle that is created by two chords or arcs meeting at a point on the circumference of a circle. We can, therefore, describe a subtended angle as the angle made from a given point. Arc APB or chord AB subtends angle C at the circumference Arc APB or chord AB subtends Angle AOB at the centre of the circle

Theorem 2 ❖ The angle subtended by an arc at the centre of a circle is double the size of the angle subtended by the same arc at the circle (on the same side of the chord as the centre) ❖ If an arc or chord subtends an angle at the centre of a circle and also at any point on the circumference, then the angle at the centre is twice angle at the circumference