Mateo Pelaez
October 24, 12
Tony Kulla
Geometry
GEOMETRY TASK #1 • Parallel Streets
1. Suppose you want to determine whether the streets represented by lines m, n, and p are parallel. What
information would you need? Explain your reasoning .
If the corresponding angles are congruent then you can determine whether the streets can be
represented by lines m,n, and p would be parallel. For example, if <1 and <4 are congruent then you
know that lines m and p are parallel lines. Corresponding angles are able to fit in the different groups of
angles in the same position.
2. Suppose that the streets represented by lines d and e are parallel. If the m ∠5 = 112°, find the m ∠ 4.
Explain how you determined the measure.
The measure of ∠ 4 is 68. By showing that the straight angle that make up a set of linear pairs that
create a straight angle 180° are both ∠ 4 and ∠ 5. This shows that measure of ∠ 4 added with the measure
of ∠ 5 will create a straight angle. By knowing these measures there is a relationship of lines d and e
being parallel.
3. If m ∠1 = 3x – 7 and m ∠4 = 2x + 20, find the value of x so that lines m and p are parallel. Explain
how you arrived at your answer and describe why these measures allow you to determine that lines m and
p are parallel.
Both ∠ 1 and ∠ 4 are set equal to each other. An example of this is that you can take ∠ 1 and
create a corresponding angle that allows you to see the that ∠ 1 and ∠ 4 are both equally set up which
then can determine whether measures are allowed to determine that lines m and p are parallel. The
measure of angles 1 and 4 are both 74 degree angles which shows that they create the same or congruent
measurement.
4. Todd wants to go from the library to his house. If the streets represented by m and n are parallel, Using
a straightedge and protractor, construct the shortest distance between the Library at “B” and the street he
lives on, n. Explain your reasoning.
The shortest distance between the library at point B is if you go up and take a right 90 on lines m
and go straight which creates a 180 which will get you to the library B. M and N are parallel because
they are both corresponding angles and have the same measurement because the lines are parallel which
makes them congruent. This is the shortest distance because it creates a faster route to take while others
may take a longer time to getting to the library or point B.