Math part 2
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the ratio of areas of two Triangles is equal to the ratio of products of their bases and corresponding Heights
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areas of triangles with equal Heights are proportional to their corresponding bases
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areas of triangles with equal bases are proportional to their corresponding height
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basic proportionality theorem
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If a line parallel to the side of a triangle intersects the remaining side in the two distinct points then the line divides the side in the same proportion
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Property of an angle bisector of a triangle
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The bisector of an angle of a triangle divides the side opposite to the angle in the ratio of the remaining sides.
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Property of three parallel lines and their transversals.
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The ratio of the intercepts made on a transversal by three parallel lines is equal to the ratio of the corresponding intercepts made on any other transversal by the same parallel lines.
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The theorem of areas of similar triangle
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When two triangles are similar, the ratio of areas of those triangles is equal to the ratio of the squares of their corresponding sides.
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If acute angles of a right-angled triangle are 30 degrees and 60 degrees, then the side opposite 30-degree angle is half of the hypotenuse, and the side opposite to 60-degree angle is root 3 upon 2 times the hypotenuse.
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If the acute angles of a right-angled triangle are 45 degrees and 45 degrees, then each of the perpendicular sides is 1 upon root 2 times the hypotenuse.
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The theorem of geometric mean
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In a right-angled triangle, the perpendicular segment to the hypotenuse from the opposite vertex is the geometric mean of the segments into which the hypotenuse is divided.
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Tangent theorem
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A tangent at any point of a circle is perpendicular to the radius at the point of contact.
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Tangent segment theorem
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Tangent segments drawn from an external point to a circle are congruent.
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The point of contact of the touching circles lies on the line joining their centers.
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The distance between the centers of the circles touching internally is equal to the difference of their radii.
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If the circles touch each other externally, the distance between their centers is equal to the sum f their radii.
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The chords corresponding to congruent arcs of a circle ( or congruent circles ) are congruent.
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Corresponding arcs of congruent chords of a circle ( or congruent circles) are congruent.
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Inscribed angle theorem
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The measure of an inscribed angle is half of the measure of the arc f the arc intercepted by it.
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The theorem of a cyclic quadrilateral.
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Opposite angles of a cyclic quadrilateral are supplementry.
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A theorem of an external division of chord.
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Tangent secant segment theorem .
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Distance formula.
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Section formula
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Midpoint formula
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Centroid formula
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The slope of the line.
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Trigonometry ratio.
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Relation between trigonometric ratio.
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Trigonometric identities
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Values of the trigonometric ratio of angles.
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Cuboid
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Cube
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Cylinder
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Cone.
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Sphere
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Hemisphere
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Frustum of cone
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Area of segment
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The sector of a circle.
