1. Basic Constructions
Skill 06

2. Objective
HSG-GPE.12: Students are responsible for making basic constructions with a straight edge and compass.

3. Definitions A straightedge is a ruler with no markings on it.
A compass is a geometric tool used to draw circles and parts of circles called arcs.
A construction is a geometric figure drawn using a straightedge and a compass.

4. Definitions
Perpendicular lines are two lines that intersect to form right angles.
A perpendicular bisector of a segment is a line, segment, or ray that is perpendicular to the segment at its midpoint.

5. Example 1; Construct Congruent Segments
Construct a segment congruent to a given segment.
𝐺𝑖𝑣𝑒𝑛: 𝐴𝐵 𝐶𝑜𝑛𝑠𝑡𝑟𝑢𝑐𝑡: 𝐶𝐷 ≅ 𝐴𝐵
1) Draw a ray with endpoint C.
2) Open compass to length of 𝐴𝐵 .
3) Use that length with end on point C, draw and arc to intersect the ray.
4) Label intersection, point D.
Therefore, 𝑪𝑫 ≅ 𝑨𝑩 .

6. Example 2; Construct Congruent Angles
Construct an angle congruent to a given angle.
𝐺𝑖𝑣𝑒𝑛: ∠𝐴 𝐶𝑜𝑛𝑠𝑡𝑟𝑢𝑐𝑡:∠𝑆≅∠𝐴
1) Draw a ray with endpoint S.
2) With compass on point A, draw an arc that intersects both sides label, B and C.
3) With same compass setting and end on S, draw an arc and label the intersection R.
4) Open compass to length BC, use compass setting with end on R. Draw and arc intersecting previous arc, label point T.
5) Draw 𝑆𝑇
Therefore, ∠𝑺≅∠𝑨.

7. Example 3; Construct Perpendicular Bisector
Construct a perpendicular bisector to the given segment.
𝐺𝑖𝑣𝑒𝑛: 𝐴𝐵
𝐶𝑜𝑛𝑠𝑡𝑟𝑢𝑐𝑡: 𝑋𝑌 such that 𝑋𝑌 ⊥ 𝐴𝐵 and 𝐴𝑀 ≅ 𝐵𝑀 .
1) Put compass end on A. draw big arc, in which opening is greater than 1 2 𝐴𝐵.
2) Using same compass setting, put compass end on B, draw big arc so that arcs intersect.
3) Label intersections X and Y.
4) Draw 𝑋𝑌 , label intersection M.
Therefore, 𝑿𝒀 ⊥ 𝐴𝐵 & 𝐴𝑀 ≅ 𝐵𝑀 .

8. Example 4; Construct Angle Bisector
Construct an angle bisector of the given angle.
𝐺𝑖𝑣𝑒𝑛:∠𝐴
𝐶𝑜𝑛𝑠𝑡𝑟𝑢𝑐𝑡: 𝑋𝑌 such that 𝑋𝑌 ⊥ 𝐴𝐵 and 𝐴𝑀 ≅ 𝐵𝑀 .
1) Put compass end on A, draw arc intersecting both angle sides, label B and C.
2) Put compass on B, draw arc.
3) Using same compass setting, put compass on C, draw arc, label intersection D.
4) Draw 𝐴𝐷
Therefore, 𝑨𝑫 is the bisector of ∠𝑪𝑨𝑩.

9. #06: Basic Constructions
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