Chapter 4
Study Guide
I.
Distance Formula:
√(𝑥2 − 𝑥1)2 + (𝑦2 − 𝑦1)2
II.
Theorems and Postulates
A. Triangle sum Theorem: The sum of the measures of the interior angles
of a triangle is 180°
B. Exterior Angle Theorem: The measure of the exterior angle of a
triangle is equal to the sum of the measures of the two nonadjacent
interior angles
C. Side-Side-Side (SSS): If three sides of a triangle are congruent to
another, then the two triangles are congruent
D. Side-Angle-Side (SAS): If two sides and the included angle of a
triangle are congruent to another triangle, then the triangles are
congruent
E. Angle-Side-Angle (ASA): If two angles and the included side of a
triangle are congruent to another triangle, then the two triangles are
congruent.
F. Hypotenuse-Leg: If the hypotenuse and another leg on a right triangle
are congruent to another triangle, then the triangles are congruent.
G. Angle-Angle-Side (AAS): If two angles and a non-included side in one
triangle are congruent to another triangle, then the triangles are
congruent.
H. Corresponding Parts of Congruent Triangles are Congruent CPCTC: If
two triangles are congruent, then their corresponding parts are
congruent.
I. Base Angles Theorem: If two sides of a triangle are congruent, then
the angles opposite them are congruent
J. Converse on Base Angles Theorem: If two angles of a triangle are
congruent, then the sides opposite them are congruent
III.
Transformations
A. Translation: An object on a coordinate plane can be moved (slide), by
adding the same constant to every x-coordinate and adding the same
constant to every y-coordinate.
(x,y)  (x + a, y + b)
B. Reflections:
1. Across the x-axis: Multiply every y-coordinate by -1
2. Across the y-axis: Multiply every x-coordinate by -1
IV.
Useful Postulates, Theorems, and Properties from Previous Chapters
A. Vertical Angles
B. Linear Pairs
C. Angles Created by Parallel Lines & a Transversal:
1. Corresponding Angles
2. Alternate Interior Angles
3. Alternate Exterior Angles
4. Consecutive Interior Angles
D. Reflexive Property
E. Symmetric Property
F. Transitive Property
G. Definition of a Midpoint