Chapter 4: triangle congruence

1. 4-2: classifying triangles

1.1. Acutie triangle - 89 degrees or less

1.1.1. Obtuse triangle- 91-180 degrees

1.1.2. Right triangle- 90 degrees

1.1.2.1. Equilateral triangle- all 3sides are equal.

1.2. Isosceles triangle- 2 sides are the same length but the third one is larger or smaller

1.3. Equiangular triangle- each angle of your triangle are the same. Ex: 60x3(sides)=180.

1.4. Scalene triangle- 3 unequal sides but all =180

2. 4-4: congruent triangles

2.1. Corresponding angles-occupy the same relative positions: intercept at straight lines.

2.2. Corresponding sides- having a pair of matching angles that are in the same spot in two different shapes.

2.3. Congruent polygons -same number of sides, all corresponding sides and the interior angles are congruent.

3. 4-5: triangle congruence:SSS and SAS

3.1. Triangle rigidity-

4. 4-7: CPCTC

4.1. Corresponding parts of congruent triangles are congruent.

5. 4-9: isosceles and equatorial triangles

5.1. legs of an isosceles triangle- the 2 equal sides

5.2. triangle- All sides = 180 degrees.

5.3. vertical angle-each of the pairs of opposite angles made by two intersecting lines

5.4. base-The lowest part or bottom.

5.5. base angles-an isosceles triangle, the angles opposite the congruent sides are congruent.

6. 4-1: congruence and transformations.

6.1. Dilation- stretches and shrinks the original figure.

6.2. Isometry- basically are rotations, translations, reflections, glides and the identify map.

6.3. Rigid transformations- a transformation that does not change the size or shape of a figure- (reflections,rotations and translations)

7. 4-3: angle relationships in triangles

7.1. Auxiliary line- an extra line needed to complete a proof in plane geometry

7.2. Corollary-an equilateral triangle that is also equiangular.

7.3. Interior- inside

7.4. Exterior- outside

7.5. Interior angle- the angle between adjacent sides of a rectilinear figure

7.6. Exterior angle- formed by extending one of the sides or a triangle.

7.7. Remote interior angle-something that a triangle has 2 of.

8. 4-6:Triangle congruence: ASA,AAS and HL

8.1. included side-one link that links 2 angles together.

9. 4-8: introduction to coordinate proof

9.1. coordinate proof- uses generalized points. assigning variables to the coordinates.