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10-5 Special Segments

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10-5 Special Segments

Z

Divide a segment into a given number of congruent parts.

A

B

1) Choose point not on line, connect to one endpoint.

2) Use any radius, and make as many segments as you want. (I’ll do FOUR, your book has three)

Justification: If three parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal (pg 177)

3) Connect from last radius to other endpoint.

4) Construct parallel lines. (copy angle, extend line)

(not showing parallel const)

Given three segments, make a 4th so they are all proportional.

I

H

J

T

R

4) Connect RT

a

b

c

x?

a

b

c

1) Draw an angle (any size, make sides fairly long)

X

This is x, makes the proper proportion

2) On one side, mark a and b

3) On the other side, mark c

Justification: Same as before.

5) Make parallel from the end of b (Parallel construction not shown)

Given two segments, make the geometric mean.

a

b

Idea is to set up a geometric mean altitude style picture.

x

1) Draw a line and copy a and b on it.

a

b

2) Find midpoint by perpendicular bisector. (Perpendicular bisector construction not shown)

Justification, geo mean with alt. (rt angles with inscribed triangle in semi, altitude)

3) Draw semicircle by making endpoint and midpoint as radius.

4) Draw perpendicular from where a and b meet (construction of perpendicular from point on the line, not shown)

HW #23: Pg 398: CE 3, 6, 7

Pg 399: 1, 2, 5, 7-9, 11, 13-15, 17

Quiz will be limited to 10-1 to 10-4.

I ‘may’ ask if these constructions today are Euclidean or not.