Lesson 3 U6
RCSD Geometry Local MATHEMATICS CURRICULUM
Name:___________________________________
Period:_______ Date:_____________
GEOMETRY
Lesson 3: Construct regular polygons and inscribed polygons
Learning Target: I can construct regular inscribed polygons
Opening Activity
Construct an Equilateral Triangle with a side measurement of 4 cm, label it ∆𝐴𝐵𝐶. You will need a compass
and a straightedge.
Steps for construction a equilateral triangle
1.
2.
3.
4.
Draw a segment 𝐴𝐵.
̅̅̅̅.
Draw circle 𝐴: center A, radius 𝑨𝑩
̅̅̅̅.
Draw circle 𝐵: center B, radius 𝑩𝑨
Label one of intersections as 𝐶; connect points 𝐴, 𝐵, 𝐶 .
Quick write: Why do you think ∆𝐴𝐵𝐶 is an equilateral triangle? Explain your answer
Vocabulary
Regular polygon: A polygon has all __________ and __________ measurement __________.
Some examples would be
Inscribed polygon: A polygon constructed on a _____________ where every _____________ is on the circle.
Lesson 3 U6
RCSD Geometry Local MATHEMATICS CURRICULUM
Name:___________________________________
Period:_______ Date:_____________
GEOMETRY
Example 1. Construct regular hexagon inscribed in circle T shown below. [Leave all construction marks.]
http://www.bing.com/videos/search?q=constructing+regular+inscribed+hexagon&qpvt=constructing+regular
+incribed+hexagon&FORM=VDRE#view=detail&mid=923BE564165C1B4A385E923BE564165C1B4A385E
Steps for constructing inscribed hexagon
1_________________________________________________________________________________________
2_________________________________________________________________________________________
3_________________________________________________________________________________________
4_________________________________________________________________________________________
Example 2 Construct a regular hexagon in the space at
right. Follow the steps below
1.
Draw circle 𝐾: center 𝐾, any radius.
2.
Pick a point on the circle; label this point 𝐴.
Draw circle 𝐴: center 𝐴, radius ̅̅̅̅
𝐴𝐾 .
3.
5.
Label the intersections of circle 𝐴 with circle 𝐾 as 𝐵 and 𝐹.
Draw circle 𝐵: center 𝐵, radius ̅̅̅̅
𝐵𝐾 .
6.
Label the intersection of circle 𝐵 with circle 𝐾 as 𝐶.
7.
Continue to treat the intersection of each new circle with
circle 𝐾 as the center of a new circle until the next circle to be
drawn is circle 𝐴.
̅̅̅̅ , 𝐶𝐷
̅̅̅̅ , 𝐷𝐸
̅̅̅̅.
̅̅̅̅ , ̅̅̅̅
Draw ̅̅̅̅̅
𝐴𝐵, 𝐵𝐶
𝐸𝐹 , 𝐹𝐴
4.
8.
RCSD Geometry Local MATHEMATICS CURRICULUM
Name:___________________________________
Lesson 3 U6
Period:_______ Date:_____________
GEOMETRY
Example 3. Construct an equilateral triangle inscribed in circle T shown below. [Leave all construction marks.]
Steps for constructing inscribed equilateral triangle
1_________________________________________________________________________________________
2_________________________________________________________________________________________
3_________________________________________________________________________________________
4_________________________________________________________________________________________
Classwork
1. Use a compass and straightedge to construct an inscribed hexagon in circle T shown below. [Leave all
construction marks.]
Lesson 3 U6
RCSD Geometry Local MATHEMATICS CURRICULUM
Name:___________________________________
Period:_______ Date:_____________
2. Build an equilateral triangle with a side of 5 cm
3. Construct a circle and inscribe an equilateral triangle within it.
4. ∆𝐴𝐵𝐶 is shown below. Is it an equilateral triangle? Justify your response.
GEOMETRY