Download Geometry - Unit 2 - Lesson 2.5 - Properties of Parallel Lines

Geometry
Name: _______________________________
Unit 2: Lesson 2.5
Date: _________________ Period: _______
Properties of Parallel Lines
Essential Questions:
o
When two parallel lines are cut by a transversal, how can one angle measure be used to determine the
others?
Goal:
 I will discover that there is an algebraic relationship exists between special angle pairs formed by
parallel lines and a transversal.
Key Ideas/Vocabulary:
 Transversal – a line that intersects _________ or more coplanar lines at different points.
Theorems/Postulates:

Corresponding Angles Postulate – If two parallel lines are cut by a transversal, then the pairs of
corresponding angles are ________________.

Alternate Interior Angles Theorem – If two parallel lines are cut by a transversal, then the pairs of
alternate interior angles are ___________________.

Consecutive Interior Angles Theorem (Same-Side Interior) – If two parallel lines are cut by a
transversal, then the pairs of consecutive interior angles are ________________________.

Alternate Exterior Angles Theorem – If two parallel lines are cut by a transversal, then the pairs of
alternate exterior angles are ___________________.

Perpendicular Transversal Theorem – If a transversal is perpendicular to one of two parallel lines, then
it is _______________________ to the second.

Consecutive Exterior Angles Theorem (Same-Side Exterior) – If two parallel lines are cut by a
transversal, then the pairs of consecutive exterior angles are ________________________.
Section 1: Naming Pairs of Angles
1) Identify each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior
angles.
xy
ab
YT 1) Identify each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive
interior angles.
lm
Section 2: Determine Angle Measures
2) In the figure, x y and m11 51 .
YT 2) In the figure, x y and m13  143 .
Find all the missing angles.
Find all the missing angles.
Answer:
Answer:
Section 3: Find Values of Variables Using Algebra
3)
YT 3)
Answer:
4) If m5  2 x  10, m6  4 y  25, and
m7  x  15 , find x and y.
Answer:
YT 4) If m1 9 x  6, m2  25x  3, and
m3  5 y  14 , find x and y.
Answer:
Answer:
5)
YT 5) Find x and mGBA.
Answer:
Answer:
Section 4: Identify Angles Using Parallel Lines
6) Find x and y in the diagram.
YT 6) Find the measure of angle 1.
Answer:
Answer:
Homework:
Textbook: Pg. 137 – 138 # 1 – 14, # 18 – 22
Lesson Summary:
Lines m and n are cut by a transversal so that ∠2 and ∠5 are corresponding angles. If
m∠2 = (x + 18)° and m∠5 = (2x - 28)°, which value of x makes lines m and n parallel?