The line between points X and Y is a line segment. These are some of the basic theorems on the chords and arcs of a circle. In the above diagram, the angles of the same color are equal to each other.

For easily spotting this property of a circle, look out for a triangle with one of its … radii) – a line segment joining its centre to any point on the circle Chord – a line segment joining any two points on the circle Tangent line – a line which touches the circle at exactly one point You can sum up the above definitions and theorems with the following simple, concise idea. The converse of the theorem in #9 is “if a point is equidistant from the endpoints of a line segment, then the point is on the perpendicular bisector of the line segment”. The intercept theorem, also known as Thales' theorem (not to be confused with another theorem with the same name) or basic proportionality theorem, is an important theorem in elementary geometry about the ratios of various line segments that are created if two intersecting lines are intercepted by a pair of parallels.It is equivalent to the theorem about ratios in similar triangles. Some of the worksheets below are Geometry Postulates and Theorems List with Pictures, Ruler Postulate, Angle Addition Postulate, Protractor Postulate, Pythagorean Theorem, Complementary Angles, Supplementary Angles, Congruent triangles, Legs of an isosceles triangle, … We are given line segment H M and we have bisected it (divided it exactly in two) by a line W A. You can apply the Triangle Proportionality Theorem to construct a point along a directed line segment that partitions the segment in a given ratio. [Image will be Uploaded Soon] In the above figure, OD ⊥ AB, as per the theorem, hence, AD = DB. Converse: Tangent-Chord Theorem. A line segment is a part of a line which has two end points. Same-side exterior angles: Angles 1 and 7 (and 2 and 8) are called same-side exterior angles — they’re on the same side of the transversal, and they’re outside the parallel lines. The alternate segment theorem (also known as the tangent-chord theorem) states that in any circle, the angle between a chord and a tangent through one of the end points of the chord is equal to the angle in the alternate segment. Pythagoras' theorem can be used to calculate the distance between two points. Before we start talking about circle theorems we need to be familiar with these words: Diameter – the longest chord that joins two points on the circle and goes through the centre Radius (pl. Circle Theorems (aiming for a B grade and beyond) This video involves looking at a couple of circle theorem questions. This means that they all lie on the same circle. We will read about some other theorems …

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