Download Handout 1 Math 121 01/17/2016 3.4

Handout 1
Math 121
01/17/2016
3.4 - Proving Theorems About Parallel and Perpendicular Lines
THEOREM 3.4-1: Perpendicular Transversal Theorem In a plane, let two lines be cut by
a transversal. If the transversal is perpendicular to one of the parallel lines, then it is perpendicular
to the other parallel line.
THEOREM 3.4-2: Two Lines Parallel to a Third Line If two lines are parallel to the
same line, then all three lines are parallel to each other.
THEOREM 3.4-3 If two lines are perpendicular, then they intersect to form four right angles.
THEOREM 3.4-4 If two lines intersect to form a linear pair of congruent angles, then the
lines are perpendicular to each other.
4.1 - Types of Triangles
VOCABULARY
• triangle
• vertex
• opposite side and an- • obtuse triangle
gle
• equiangular triangle
• equilateral triangle
• interior angle
• sides of a triangle
• included side and an- • right triangle
gle
• scalene triangle
• exterior angle
• adjacent sides
• acute triangle
• corollary
• isosceles triangle
THEOREM 4.1-1: Triangle Angle-Sum Theorem The sum of the measures of the interior
angles of a triangle is 180◦ .
COROLLARY 4.1-2: Exterior Angle of a Triangle The measure of each exterior angle of
a triangle equals the sum of the measures of its two nonadjacent interior angles.
COROLLARY 4.1-3: Acute Angles of a Right Triangle The two acute angles of a right
triangle are complementary.
4.2 - Congruent Figures
THEOREM 4.2-1: Third Angles Theorem If two angles of one triangle are congruent to
two angles of another triangle, then the third angles are congruent.
4.3 - Congruent Triangles by SSS and SAS
POSTULATE 4.3-1: Side-Side-Side (SSS) Postulate If the three sides of one triangle are
congruent to the three sides of another triangle, then the two triangles are congruent.
POSTULATE 4.3-2: Side-Angle-Side (SAS) Postulate If two sides and the included
angle of one triangle are congruent to two sides and the included angle of another triangle, then the
two triangles are congruent.
4.4 - Congruent Triangles by ASA and AAS
POSTULATE 4.4-1: Angle-Side-Angle (ASA) Postulate If two angles and the included
side of one triangle are congruent to two angles and the included side of another triangle, then the
two triangles are congruent.
THEOREM 4.4-2: Angle-Angle-Side (AAS) Theorem If two angles and a non included
side of one triangle are congruent to two angles and the corresponding non included side of another
triangle, then the triangles are congruent.
Winter 2017
Los Angeles City College
G. Dekermenjian