Sorry a little numbering problems
Ok... a little more Geometry
By Miyu.
A = C
B D
Extremes: A and D
Means: C and B
Cross Products: The product of the means and the product of the extremes. In other words, if A/B=C/D
then ad=bc
Similar: Two Figures that have the same shape, but not necessarily the same size, are similiar.
Similarity Statement: A statement indicating that two polygons are similar by listing their vertices in order of correspondence. (In the same order)
Theorems:
1.Through a line and a point not on the line, there exist exactly one perpendicular line to the given line.
2.The perpendicular segment from a point to a line is the shortest segment from the point to the line.
3.The perpendicular segment from a point to a plane is the shortest segment from the point to the plane.
4.If two lines are parallel, then all points on one line are equidistant from the other line.
5.If a diameter is perpendicular to a chord, then it bisects the chord and its arcs
6.If a diameter bisects a chord other than another diameter then it is perpendicular to the chord.
7.The perpendicular bisector of a chord contains the center of the circle.
8.In a circle or congruent circles:
Chords equidistant from the center are congruent.
Congruent chords are equidistant from the center of the circle.
9.If two polygons are similar, then the ration of their perimeters is equal to the ratio of their corresponding sides.
Postulate:(AA)(ANGLE ANGLE):If two angles of one triangle are congruent to two angles of another triangle, then the triangle are similar
Theorem: SSS Similarity Theorem: If the length of the sides of a triangle are proportional to the lengths of the sides of another triangles are similar
SAS Similarity Theorem: If two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, then the triangles are similar
Inscribed Angles: An angle whose vertex is on a circle and whose sides contain chords of the circle.
The arc formed by an inscribed angle is the intercepted arc of that angle.
The measure of an inscribed angle is equal to half the measure of its intercepted arc.
If an inscribed angle intercepts a semicircle, then it is a right angle.
If two inscribed angles intercept the same arc, then they are congruent.
If a quadrilateral is inscribed in a circle, then it has supplementary opposite angles.
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Thursday, July 12, 2012
Sunday, July 8, 2012
Thursday, July 5, 2012
Issue 21: Geometry
By Miyu:
WELL... It is the hot humid summer but we still have to keep studying to keep up the good work. More Geometry （ｏ。ｏ；）☆⌒(*＾-°)v
So... ISSUE 21: Geometry.
Arc Length: Distance along an arc measured in linear units
<<< Here's a picture I found on google that could help you. (This isn't a photo made by me, just a good photo to use)
Sector of a circle: The region inside a circle bounded by two radii of the circle and their intercepted
arc.
<<<More good pictures and information.
Incenter of the triangle: When all 3 angels of a triangle are bisected, the point of concurrency.
If a line bisects an angle of a triangle, then it divides the opposite side proportionally to the other 2 sides of the triangle.
If perpendicular bisectors are drawn for every side of a triangle, the point of concurrency is the circumcenter of the triangle.
The circumcenter lies at the center of the circle that contains the three vertices of the triangle. Any circle that contains all the vertices of a polygon is called a circumscribed circle. Any Polygon with each vertex on a circle is an inscribed polygon
Theorem 39-1: If one side of a triangle is longer than the other side, then the angle opposite the first side is larger than the angle opposite the first side is larger than the angle opposite the second side.
Theorem 39-2: If one angle of a triangle is larger than another angle, then the side opposite the first angle is longer than the side opposite the second angle.
Theorem 39-3: Exterior Angle Inequality Theorem: The measure of an exterior angle is greater than the measure of either remote interior angle.
Theorem 39-4: The sum of the length of any two sides of a triangle must be greater than the length of the third side.
Postulate 19: If two polygons are congruent, then they have the same area.
Postulate 20: The area of a region is equal to the sum of the areas of its nonoverlapping parts.
Theorem 40-1: Hinge Theorem- If two sides of one triangle are congruent to two sides of another triangle and the included angle of the first triangle is greater than the included angle of the second triangle, then the third side of the first triangle is longer than the third side of the second triangle.
Theorem 40-2: Converse of the Hinge Theorem: If two sides of one triangle are congruent to two sides of another triangle and the third side of the first triangle is longer than the third side of the second triangle.
**EDIT**
Measure of central angle = Measure of arc.
(A friend assured me... LOL)
WELL... It is the hot humid summer but we still have to keep studying to keep up the good work. More Geometry （ｏ。ｏ；）☆⌒(*＾-°)v
So... ISSUE 21: Geometry.
Arc Length: Distance along an arc measured in linear units
Sector of a circle: The region inside a circle bounded by two radii of the circle and their intercepted
arc.
Incenter of the triangle: When all 3 angels of a triangle are bisected, the point of concurrency.
If a line bisects an angle of a triangle, then it divides the opposite side proportionally to the other 2 sides of the triangle.
If perpendicular bisectors are drawn for every side of a triangle, the point of concurrency is the circumcenter of the triangle.
The circumcenter lies at the center of the circle that contains the three vertices of the triangle. Any circle that contains all the vertices of a polygon is called a circumscribed circle. Any Polygon with each vertex on a circle is an inscribed polygon
Theorem 39-1: If one side of a triangle is longer than the other side, then the angle opposite the first side is larger than the angle opposite the first side is larger than the angle opposite the second side.
Theorem 39-2: If one angle of a triangle is larger than another angle, then the side opposite the first angle is longer than the side opposite the second angle.
Theorem 39-3: Exterior Angle Inequality Theorem: The measure of an exterior angle is greater than the measure of either remote interior angle.
Theorem 39-4: The sum of the length of any two sides of a triangle must be greater than the length of the third side.
Postulate 19: If two polygons are congruent, then they have the same area.
Postulate 20: The area of a region is equal to the sum of the areas of its nonoverlapping parts.
Theorem 40-1: Hinge Theorem- If two sides of one triangle are congruent to two sides of another triangle and the included angle of the first triangle is greater than the included angle of the second triangle, then the third side of the first triangle is longer than the third side of the second triangle.
Theorem 40-2: Converse of the Hinge Theorem: If two sides of one triangle are congruent to two sides of another triangle and the third side of the first triangle is longer than the third side of the second triangle.
**EDIT**
Measure of central angle = Measure of arc.
(A friend assured me... LOL)
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