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UNIT 1 • SIMILARITY, CONGRUENCE, AND PROOFS
Lesson 3: Constructing Polygons
Lesson 1.3.2: Constructing Squares Inscribed in Circles
Warm-Up 1.3.2
Antonia is making four corner tables, one for each of her three sisters and herself. She has one large
square piece of wood that she plans to cut into four tabletops. She begins by marking the needed cuts
for the tabletops on the square piece of wood.
1. E ach angle of the square piece of wood measures 90˚. If Antonia bisects one angle of the square,
what is the measure of the two new angles?
2. B
isect one angle of the square. Extend the angle bisector so that it intersects the square in two
places. Where does the bisector intersect the square?
3. B
isect the remaining angles of the square. If Antonia cuts along each angle bisector, what figures
will she have created?
4. What are the measures of each of the angles of the new figures?
U1-161
© Walch Education
CCGPS Analytic Geometry Teacher Resource
UNIT 1 • SIMILARITY, CONGRUENCE, AND PROOFS
Lesson 3: Constructing Polygons
Instruction
Lesson 1.3.2: Constructing Squares Inscribed in Circles
Common Core Georgia Performance Standard
MCC9–12.G.CO.13
Warm-Up 1.3.2 Debrief
Antonia is making four corner tables, one for each of her three sisters and herself. She has one large
square piece of wood that she plans to cut into four tabletops. She begins by marking the needed cuts
for the tabletops on the square piece of wood.
1. E ach angle of the square piece of wood measures 90˚. If Antonia bisects one angle of the square,
what is the measure of the two new angles?
When an angle is bisected, it is divided into two equal angles.
90 ÷ 2 = 45
Each of the new angles measures 45˚.
2. B
isect one angle of the square. Extend the angle bisector so that it intersects the square in
two places. Where does the bisector intersect the square?
The angle bisector intersects the square at the bisected angle and the angle opposite the
bisected angle.
U1-162
CCGPS Analytic Geometry Teacher Resource
© Walch Education
UNIT 1 • SIMILARITY, CONGRUENCE, AND PROOFS
Lesson 3: Constructing Polygons
Instruction
3. B
isect the remaining angles of the square. If Antonia cuts along each angle bisector, what figures
will she have created?
Antonia will have created 4 triangles.
4. What are the measures of each of the angles of the new figures?
Each triangle will have two 45˚ angles and one 90˚ angle.
Connection to the Lesson
•
Students will practice geometric constructions by bisecting angles.
•
Students will also learn more about squares in this lesson.
U1-163
© Walch Education
CCGPS Analytic Geometry Teacher Resource