Download Construction Homework: Higher Geometry FOR EACH PROBLEM

Construction Homework: Higher Geometry
FOR EACH PROBLEM, PROVIDE A CLEARLY WRITTEN EXPLANATION OF
YOUR STEPS. Your directions may reference one of the standard constructions we
discussed in class (see list below). Please include all compass markings, etc.
STANDARD CONSTRUCTIONS
1.
2.
3.
4.
5.
6.
7.
Duplicate a segment
Duplicate an angle
Construct a perpendicular bisector of a segment
Construct a perpendicular to a given line through a point not on the line
Construct a perpendicular to a given line through a point on the line
Construct an angle bisector
Given a line l, and a point P not on l, construct a line through P that is parallel to l
PROBLEMS:
1. Use the two segments shown below to construct a line segment with length AB + 2 CD. You
may label your new segment as you wish. AS FOR ALL PROBLEMS, BE SURE THAT YOUR
COMPASS MARKINGS SHOW.
D
C
2. Draw two acute angles on your paper. Construct a third angle with a measure equal to the
sum of the measures of the first two angles. Remember that you may use only a compass and
straightedge. Use labels as you wish.
3. Construct an equilateral triangle, given the length of one side (see CD below). Use only a
compass and straightedge.
D
C
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4. Draw and label a segment as PQ. Divide PQ into four congruent segments, using only a
compass and straightedge.
5. Draw a triangle. Label it ABC. Construct the perpendicular bisector of each side, using only
compass and straightedge. What do you observe?
6. Repeat the directions in example 6, but draw the medians of each side instead.
7. Draw an acute triangle. Label it ABC. Construct the altitude CD, using only compass and
straightedge.
8. Draw an obtuse triangle. Label it DEF, with the obtuse angle at D. Using only compass and
straightedge, construct all three altitudes to the triangle. Label them DP, EQ and FS. (Note: to
construct an altitude to certain sides, it will be necessary to first extend the side.) In an obtuse
triangle, how many altitudes fall outside of the triangle?
9. Draw a segment. Label it PQ. Using only compass and straightedge, construct a square with
PQ as one of its sides.
10. Construct an angle with each given measure and label it. Remember to only use a compass
and straightedge ---No protractor!
a) 90 °, b) 45 °, c) 135 °
11. Use a compass and straightedge only. Draw a line and a point not on this line. Draw any
transversal to the first line that passes through this point. (Do not choose a perpendicular
transversal.) Construct a second line parallel to the first line, by duplicating alternate interior
angles.
12. Draw an acute angle ∠C and a segment PQ on your paper. Construct a rhombus with the
length of PQ as its side length and the measure of ∠C as one of its acute angles. Remember
that you may use only a compass and straightedge.
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