Geometry
Unit 1 Part 1: WS 1: Page 3 1-10
Name________________________________
Date________________ Period_____ #_____
Lesson Objectives and Notes: Section 1-1 (G.2.2.1.1):
 Students will use the term equidistant.
 Students will use deductive reasoning to prove facts about a diagram.
1. Do the slants lie on the same line?
2. Are the horizontal lines parallel?
Deductive Reasoning: _____________________________________________________________
Equidistant: ______________________________________________________________________
Suppose that you and Pat are partners in a game in which you must locate various clues to win. You
are told to pick up your next clue at a point that is as far from the fountain as from the oak tree and is
10 m from the flag pole. You locate a point 𝑋, which satisfies both requirements, but grumble
because there isn’t any clue to be found at point 𝑋. Then Pat realizes that there may be a different
location that satisfies both requirements. Can you locate another point that meets both
requirements?
Pole
10 m
X
Equidistant
Fountain
Tree1
Suppose that you concentrate on points that are equidistant from the fountain and oak tree while Pat
works on points that are 10 m from the pole. In the diagram below, 1 cm represents 2 m, the circle
represents Pat’s points and the line represents your points. If you could not locate another location
does the diagram help in finding another point 𝑌, which meets both requirements?
Y
5 cm
Pole
Pat's Points
5 cm
X
Your Points
Fountain
Tree
Classroom Exercises: Refer to the diagram above.
1. Suppose the diagram showed all points that are 5 cm from point 𝑃. What geometric figure would
the points form? __________
2. Is there a point on the line that is 15 cm from points 𝐹 and 𝑇? _______ How many points meet
this requirement? _______
3. It appears as if points 𝑃, 𝑋 and 𝑇 might lie on a straight line. Do they? _______
4. It appears as if point 𝑃 might be equidistant from points 𝑋 and 𝐹. Is it? _______
5. Suppose Pat spoke of a line 𝑙 joining points 𝐹 and 𝑇 while you thought of a line 𝑛 joining points 𝐹
and 𝑇. Is it better to say that lines 𝑙 and 𝑛 are two different lines, or to say that they are the same
lines with different names? __________
6. Point 𝑋 is equidistant from points 𝐹 and 𝑇. Furthermore, point 𝑌 is equidistant from points 𝐹 and 𝑇.
Does that mean that points 𝑋 and 𝑌 are equally distant from point 𝐹? _______
7. Suppose you were asked to find a point 5 cm from points 𝑃, 𝐹 and 𝑇. Is there such a point?
_______
8. Do you believe there is any point that is equidistant from points 𝑃, 𝐹 and 𝑇? _______
Geometry
Unit 1 Part 1: WS 1: Page 3 1-10
Name________________________________
Date________________ Period_____ #_____
Directions: Complete.
1.
Distance Between
𝑋 and 𝑃
𝑋 and 𝐹
𝑋 and 𝑇
𝑌 and 𝐹
𝐹 and 𝑇
Diagram Distance (cm)
5 cm
7 cm
Ground Distance (m)
10 m
19 m
12 cm
Pole
Fountain
Tree
2. Using the diagram above to draw,
a. A line to indicate all points equidistant from points 𝐹 and 𝑇.
b. A circle to indicate all points 6 cm from point 𝑃.
c. How many points are equidistant from points 𝐹 and 𝑇, and are also 6 cm from point 𝑃? _______
3. Using the diagram above to draw,
a. A line to indicate all points equidistant from points 𝐹 and 𝑇.
b. A circle to indicate all points 2 cm from point 𝑃.
c. How many points are equidistant from points 𝐹 and 𝑇, and are also 2 cm from point 𝑃? _______
4. There is a distance you could use that would lead to an answer of one point for part (c) in problems
2 and 3. Estimate that distance. _______
3
Directions: First make an educated guess to answer the following questions then check by
measuring to get the answer.
T
R
S
5. Which is greater, the distance from 𝑅 to 𝑆 or the distance
from 𝑇 to 𝑈? _______
U
A
6. Which is greater, the distance from 𝐴 to 𝐵 or the distance
from 𝐴 to 𝐶? _______
B
C
7. How does the area of the outer square compare to the area
of the inner square? _______
8. Compare the areas of the shaded regions that are marked R and B?
(𝐴𝑟𝑒𝑎 𝑜𝑓 𝑎 𝑐𝑖𝑟𝑐𝑙𝑒 = 𝜋𝑟 2 ) _______
B
RR R
9. Which is greater, the product of 𝑎𝑏 or the product of 𝑐𝑑? _______
a
c
d
b
10. A path between opposite vertices of the square is made up of
hundreds of horizontal and vertical segments. What is the best
approximation to the length of the path.
24, 34, 44 or more than 44? _______
17
17
17
17