#### Math - 2018-19

# G.4abcdefgh - Constructions

G.4The student willconstructandjustifythe constructions ofa) a line segment congruent to a given line segment;

b) the perpendicular bisector of a line segment;

c) a perpendicular to a given line from a point not on the line;

d) a perpendicular to a given line at a given point on the line;

e) the bisector of a given angle;

f) an angle congruent to a given angle;

g) a line parallel to a given line through a point not on the line;

h) an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

*Adopted: 2016*

### BIG IDEAS

- I can design and draft house plans, lay out the bases for a
baseball diamond, determine safe construction with adequate support and stress
beams, create pleasing patterns for trendy fashions, animate characters for a
feature movie, and program a popular computer game.

- I will
better understand geometric concepts,
the validation of proofs, and the requirement of critical thinking and I will be
able to make drawings when direct measurement is not possible or appropriate.

### UNDERSTANDING THE STANDARD

· Construction techniques are used to solve practical problems in engineering, architectural design, and building construction.

· Construction techniques include using a straightedge and compass, paper folding, and dynamic geometry software.

· Geometric constructions assist in justifying, verifying, and visually reinforcing geometric relationships.

· There are multiple methods to most geometric constructions. Students would benefit from experiences with more than one method and should be able to justify each step of geometric constructions.

· Individual steps of constructions can be justified using angle relationships, properties of quadrilaterals, congruent triangles, and/or circles.

The construction for a line segment congruent to a given line segment can be justified using properties of a circle.

The construction for the perpendicular bisector of a line segment can be justified using the properties of quadrilaterals or congruent triangles.

The constructions for a perpendicular to a given line from a point on, or not on, the line can be justified using the properties of quadrilaterals or congruent triangles.

The constructions for the bisector of a given angle and an angle congruent to a given angle can be justified using the properties of quadrilaterals or congruent triangles.

The construction for a line parallel to a given line through a point not on the line can be justified using the angle relationships formed when two lines are intersected by a transversal.

The constructions for an equilateral triangle, square, or regular hexagon inscribed in a circle can be justified using properties of circles.

· Constructions can be completed within the context of complex figures.

### ESSENTIALS

**The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to**

·
G.4a_{1} **Construct**
and **justify** the constructions of a
line segment congruent to a given line segment;

·
G.4b_{1} **Construct**
and **justify** the constructions of the
perpendicular bisector of a line segment;

·
G.4c_{1} **Construct**
and **justify** the constructions of a perpendicular
to a given line from a point not on the line;

·
G.4d_{1} **Construct**
and **justify** the constructions of a
perpendicular to a given line at a given point on the line;

·
G.4e_{1} **Construct**
and **justify** the constructions of the
bisector of a given angle;

· G.4f _{1} **Construct** and **justify** the constructions of an angle congruent to a given angle;

· G.4g_{1}**Construct** and **justify** the constructions of a line parallel to a given line through a point not on the given line;

· G.4h_{1} **Construct** and **justify** the constructions of an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

### KEY VOCABULARY

construct,
justify, construction, line segment, perpendicular, perpendicular bisector, line, point,
bisector, angle, congruent, equilateral triangle, square, regular, hexagon,
circle, circumscribed, tangent, tangent line, straightedge/ruler, compass

*Updated: Aug 23, 2018*