CP Geometry | Unit 1: Congruence, Proof, & Construction
Name: _____________________________________
Date: _______________
Period: _______
Constructing Circles, Segments, & Bisectors: Notes and Exit Slip
What are geometric constructions?
Geometric constructions are drawings that use only ______________________________________ – NOT a _______________.
Many geometric theorems can be proved through constructions.
(1) Constructing a Circle
Example: Construct a circle with center C and radius 𝐴𝐵.
Step 1: Draw a point in the space below, and label it C.
This will be the center of the circle.
A
B
Step 2: Place the pointer on point A and extend it until it reaches point B so your compass now has a
measure of 𝐴𝐵.
Step 3: Place the point of the compass on C, and spin the compass to draw the circle. Make sure the
opening does not change at all as you draw!
Congratulations! You have just constructed a ______________________.
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(2) Copying a Segment
Example: Construct a segment with the same length as 𝐴𝐵 (below), without measuring with a ruler.
Step 1: Draw a ray that is longer than 𝐴𝐵. Label one endpoint A’.
Step 2: Set the opening of your compass to the distance AB.
Step 3: Keeping the compass at the same opening set, place the point of your compass on A’. Draw a small
arc that intersects the line segment. Label the point B’ where the arc intersects the segment. You
may want to erase the rest of the segment when constructing on your own.
A
B
Recall the definitions of = and ≅ and fill in the equality and congruence statements below:
Equality Statement: __________ = __________
Congruence Statement: __________ ≅ __________
------------------------------------------------------------  Practice ---------------------------------------------------------1. Copy 𝑪𝑫 and label your new segment 𝑪’𝑫’.
Equality Statement: __________ = __________
Congruence Statement: __________ ≅ __________
2. Create the length 𝟐𝑪𝑫. [Hint: Start by drawing a ray that is longer than two 𝐶𝐷’s combined.]
Equality Statement: 𝐶𝐷 + 𝐶𝐷 = __________
Congruence Statement: 𝐶𝐷 + 𝐶𝐷 ≅ __________
3. Construct a segment whose length is 𝑳𝑶 + 𝑵𝑮.
Equality Statement: 𝐿𝑂 + 𝑁𝐺 = __________
Congruence Statement: 𝐿𝑂 + 𝑁𝐺 ≅ __________
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CP Geometry | Unit 1: Congruence, Proof, & Construction
(3) Bisecting a Segment
Example: Construct the midpoint of line segment AB.
Step 1: Place your pointer at point A, and
extend your compass so that the distance
exceeds halfway. Create an arc.
Step 2: Without changing your compass
measurement, place your pointer at point
B and create the same arc. The two arcs
will intersect at 2 points, which you will
label C and D.
Step 3: Connect points C and D to form
.
is the perpendicular bisector of AB – it
cuts segment AB in half and meets AB at
90-degree angles.
[We will discuss this proof at a later point.]
Step 4: The intersection of
and AB is the
midpoint of AB , which we will label 𝑀.
Add tick marks to indicate 𝐴𝑀 ≅ 𝑀𝐵.
------------------------------------------------------------  Practice ---------------------------------------------------------Instructions: Construct the midpoints of segment 𝐴𝐵 by bisecting it.
1.
Equality Statement: __________ = __________
Congruence Statement: __________ ≅ __________
A
B
C
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----------------------------------------------------  Cumulative Practice -----------------------------------------------1. Construct a circle with diameter 4MS with center C.
[Hint: What is diameter compared to radius?]
2. Construct a segment whose length is XY – VW.
3. List the general steps involved with constructing a circle with diameter XY. [I summarized this
construction in 2 steps.]
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CP Geometry | Unit 1: Congruence, Proof, & Construction
3. Is it possible to construct the midpoint of a ray? Why or why not?
4. In the “Bisecting a Segment” example, construct segments to make ACBD a quadrilateral. What
specific shape is ACBD and how do you know?
----------------------------------------------------- Exit Ticket (Rip off) -----------------------------------------------------Name: _____________________________________
Date: _______________
Period: _______
1. Construct a segment whose segment is XY +MS – VW.
2. Bisect TR where
TR is given by
3. Write any question you have regarding constructions of circles, segments, and bisectors. If you
don’t have any questions, indicate which construction you would like to practice more with and
why.
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