Geometric Constructions

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Similar triangles have corresponding sides in the same proportion and corresponding angles equal. To construct a similar triangle, we use the property that the ratio of corresponding sides remains con…

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A tangent to a circle is a line that touches the circle at exactly one point. Key property: A tangent is always perpendicular to the radius drawn to the point of contact.

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1. Construct a line parallel to a given line through an external point 2. Construct perpendicular bisector of a line segment 3. Construct a triangle with given sides 4. Divide a line segment into equa…

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The first step is to identify the given triangle and the ratio in which the similar triangle needs to be constructed. Then decide whether the vertices will be distinct or if one vertex will be common …

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Case 1: When vertices are distinct - The similar triangle is constructed separately with no common vertices with the original triangle. Case 2: When one vertex is common - One vertex of the similar tr…

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The principle is that a line perpendicular to the radius at its outer end is a tangent to the circle. So we draw the radius to the given point and then construct a perpendicular line at that point.

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1. Draw a circle with center C and take point P on the circle 2. Draw ray CP 3. Draw line l perpendicular to ray CP through point P Line l is the required tangent at point P.

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The tangent-secant angle theorem and its converse are used. The theorem states that the angle between a tangent and a secant equals the inscribed angle on the opposite side of the secant.