Classwork for Constructing a Regular Hexagon, Inscribed Shapes, and Isosceles Triangle

I. Review 1) Construct a perpendicular bisector to 퐴퐵̅̅̅̅. 2) Construct a perpendicular line through point P.

P •

A B

3) Construct an equilateral triangle with length CD. (LT 1c)

C D

II. Construct a Regular Hexagon (LT 1c)

Hexagon A six-sided polygon

Regular Hexagon A six-sided polygon with all sides the same length and all interior angles the same measure

Begin by constructing an equilateral with the segment below. We can construct a regular hexagon by observing that it is made up of Then construct 5 more equilateral triangles with anchor point on point R

6 adjacent (sharing a side) equilateral for one arc and anchor point on the most recent point of intersection for the second ( intersecting) arc. triangles.

R

III. Construct a Regular Hexagon Inscribed in a Circle Inscribed (in a Circle) All vertices of the inscribed shape are points on the circle

Inscribed Hexagon Hexagon with all 6 vertex points on a circle

Construct a regular hexagon with side length 퐴퐵̅̅̅̅: A B

1) Copy the length of 퐴퐵̅̅̅̅ onto the compass.

2) Place metal tip of compass on point C and construct a circle.

3) Keep the same length on the compass.

4) Mark any point (randomly) on the circle.

C 5) Place the metal tip on the randomly marked • point and mark an arc on the circle.

6) Lift the compass and place the metal tip on the last arc mark, and mark new arc on the circle.

7) Repeat until the arc mark lands on the original point.

8) Using the straightedge, connect all arc mark points (in consecutive order) on the circle.

IV. Construct an Equilateral Triangle Inscribed in a Circle with Radius 푋푌̅̅̅̅: X Y 1) Copy the length XY onto the compass.

2) Construct a circle with radius XY and center C.

3) Make the six arc marks on the circle • like you did for the regular hexagon. C

4) Connect every other arc mark to make a triangle.

V. Practice: Construct a regular hexagon with the given side length and center point C. a) b)

•C

• C

The convenient thing about this construction is that you never have to (and you shouldn’t ever) change the setting on the compass!

c) Construct an equilateral triangle inscribed in a circle with the given radius and center point C.

radius • C

VI. Construct an Isosceles Triangle

Isosceles Triangle A triangle with two sides with the same length

1) Place anchor point on point H and construct an

arc with radius more than half the length of HI.

2) Using the same compass length as in step 1, place anchor point on point I and construct an arc that intersects the first arc. Label this point of intersection point G.

H I 3) Connect H to G, then connect I to G. VII. Practice: Construct an isosceles triangle with base (non-congruent side) ST.

1) 2) T

S S T

VIII. Perpendicular Bisector Theorem

If a point is on the perpendicular bisector of a segment, then it is equidistant from the segment's endpoints.

Example: If CP is a perpendicular bisector of AB, and AC = 8, find the length of BC.

8 x

Examples: Sketch a segment congruent to 퐴푋̅̅̅̅̅.

A 8 • X 8

• X

B 8