Basic High School Geometry Book
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chap 4
An if-then statement can be changed in many ways. The original statement is called a conditional.
An isosceles triangle, as mentioned before, has at least two congruent sides, called the legs. The side left over is called the base. The two angles that connect the legs to the base are the base angles, which are equal as mentioned in the Isosceles triangle theorem. The angle that connects the two legs is called the vertex angle. (Theorem 4-2) The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base. An equilateral triangle is also considered an isosceles triangle. The Corollary to the Isosceles triangle states that an equilateral triangle is also equiangular.
In a triangle if a segment connects two of the sides’ midpoints, it is called a midsegment. (Triangle Midsegment Theorem) If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side and half its length.
(Triangle Inequality Theorem) A triangle must have three sides of which any two when added cannot be equal or longer than the third. The angles of the triangle also are connected to the sides. (Theorem 4-10) If no two sides of a triangle are not congruent, then the larger angle lies opposite the longer side and vice-versa.
The Perpendicular Bisector Theorem states that a point located on the perpendicular bisector of a segment, it is the same distance apart from each endpoint of the segment, and so if it is equal distance from two endpoints of a segment, it is on the perpendicular bisector. (Angular Bisector Theorem) If a point is on the bisector of an angle it is also equidistant from the sides of the angle A locus is a set of points that meets a stated condition such as an equal distance from a point. It would show up as an arc or a circle.
the locus is all the points 4 inches from point p
The distance from a point to a line is the length of the perpendicular segment from the point to the line. In other words the line made from the point must make a right angle with the line being attached to.
A concurrent point is the point of intersection of three are more lines. The point is called the point of concurrency. (Theorem 4-16) The perpendicular bisectors of all the sides of a triangle are concurrent at a point equidistant from all the vertices, and (Theorem 4-17) the angle bisectors of a triangle are concurrent at a point equidistant from all the sides.
The median of a triangle is a segment whose endpoints are a vertex and the midpoint of the side opposite the vertex. The altitude of a triangle is a perpendicular segment from a vertex to the line containing the side opposite the vertex. The altitude may lie outside of an obtuse triangle. The lines that contain all of the altitudes or all of the medians of a triangle.