Basic High School Geometry Book
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chap 2
1) (Triangle Angle-Sum Theorem) The sum of the measures of a triangle is 180. An exterior angle of a polygon is an angle formed by a side and an extension of a side. Anytime you know either the angle or the exterior angle, the value of the other can be found by subtracting the number known from 180 because it would create a straight angle. If all the lines on a triangle were extended, there would be two exterior angles and one vertical angle for every vertex. For each exterior angle of a triangle, the two nonadjacent interior angles are called its remote interior angles. They are the two angles not located on the vertex of the exterior angle involved. (Exterior Angle Theorem) If the two remote interior angles were added together, they equal the exterior angles. The corollary to the exterior angle theorem states that the measure of an exterior angle of a triangle is greater than the measure of either of its remote interior angles.
An equilateral triangle contains three equal sides. An isosceles triangle contains at least two congruent sides. A scalene triangle has no congruent triangles. An equiangular triangle contains three congruent angles while an acute angle contains three acute angles. A right triangle has one right angle, and an obtuse angle has one obtuse angle.
2) A polygon is a plane that has at least three sides that must connect at the endpoints to close the plane. No sides that are adjacent can be collinear, in other words, one of the vertices cannot be found in the middle of a straight line. To name a or identify a polygon start with any vertex and list the others consecutively in either direction. If a polygon has no diagonal made from two vertices lying outside of the polygon, it is convex. If it does, the polygon is concave.
A concave most resembles a circle.
(Polygon Interior Angle-Sum Theorem) The sum of the interior angles of an n-gon is ( n - 2)180. For example, a triangles would be a 3-gon, so the interior angles ( I ) would equal ( 3 - 2) 180 which equals ( 1) 180 which equals 180; therefore, the measure of the interior angles of a triangle equal 180o. An equilateral polygon has all congruent sides, and a equiangular polygon has all congruent angles. A regular polygon is equilateral and equiangular.
4) There are some quadrilaterals that have special names. A parallelogram is a quadrilateral with both pairs of opposite sides parallel. A rhombus is a parallelogram with four congruent sides. A rectangle is a parallellogram with four right angles. A square is a parallelogram with four congruent sides and four right angles. A kite is a quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent. A trapezoid is a quadrilateral with exactly one pair of parallel sides. An isosceles trapezoid is a trapezoid whose nonparallel sides are congruent.
arc RST is a major arc
arc ST is a semicircle
segment ST is the diameter
segment PR is the radius
6) Congruent circles have congruent radii while congruent polygons have congruent corresponding parts. The matching angles and sides of congruent polygons are called corresponding parts, and matching vertices are called corresponding vertices. When you name congruent polygons all corresponding vertices must be placed in the same position ( for example: ACBX - PRQY).