# G.4abcdefgh - Constructions

G.4  The student will construct and justify the constructions of

a)  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.

### 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

2016 VDOE Curriculum Framework - G.4 Understanding

·  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.4a1  Construct and justify the constructions of a line segment congruent to a given line segment;

·  G.4b1  Construct and justify the constructions of the perpendicular bisector of a line segment;

·  G.4c1  Construct and justify the constructions of a perpendicular to a given line from a point not on the line;

·  G.4d1  Construct and justify the constructions of a perpendicular to a given line at a given point on the line;

·  G.4e1  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.4g1Construct and justify the constructions of a line parallel to a given line through a point not on the given line;

·  G.4h1 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