# 6.12 and *6.9 - Congruence

6.12    The student will determine congruence of segments, angles, and polygons.

6.9  The student will determine congruence of segments, angles, and polygons.

Bloom's Level:  Evaluate

### BIG IDEAS

• I can construct a bridge or building, tile a floor, create a quilt, and replace spindles in a railing.
• I will know that congruence describes a special similarity relationship between objects and is a form of equivalence.

### UNDERSTANDING THE STANDARD

• Congruent figures have exactly the same size and the same shape.
• Noncongruent figures may have the same shape but not the same size.
• The symbol for congruency is ≅.
• The corresponding angles of congruent polygons have the same measure, and the corresponding sides of congruent polygons have the same measure.
• The determination of the congruence or noncongruence of two figures can be accomplished by placing one figure on top of the other or by comparing the measurements of all sides and angles.
• Construction of congruent line segments, angles, and polygons helps students understand congruency.

·  The symbol for congruency is .

·  Congruent figures have exactly the same size and the same shape. Line segments are congruent if they have the same length.  Angles are congruent if they have the same measure. Congruent polygons have an equal number of sides, and all the corresponding sides and angles are congruent.

-  Examples:

·  A polygon is a closed plane figure composed of at least three line segments that do not cross.

·  A regular polygon has congruent sides and congruent interior angles.

·  The number of lines of symmetry of a regular polygon is equal to the number of sides of the polygon.

·  A line of symmetry divides a figure into two congruent parts, each of which is the mirror image of the other.  Lines of symmetry are not limited to horizontal and vertical lines.

·  Noncongruent figures may have the same shape but not the same size.

·  Students should be familiar with geometric markings in figures to indicate congruence of sides and angles and to indicate parallel sides. An equal number of hatch (hash) marks indicate that those sides are equal in length. An equal number of arrows indicate that those sides are parallel. An equal number of angle curves indicate that those angles have the same measure. See the diagram below.

·  The determination of the congruence or noncongruence of two figures can be accomplished by placing one figure on top of the other or by comparing the measurements of all corresponding sides and angles.

·  Construction of congruent line segments, angles, and polygons helps students understand congruency.

### ESSENTIALS

• Given two congruent figures, what inferences can be drawn about how the figures are related?
The congruent figures will have exactly the same size and shape.
• Given two congruent polygons, what inferences can be drawn about how the polygons are related?
Corresponding angles of congruent polygons will  have the same measure. Corresponding sides of  congruent polygons will have the same measure.

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

6.121  Characterize polygons and congruent and non­congruent according to the measures of their sides and angles.

·  6.91  Identify regular polygons.

6.122  Determine the congruence of segments, angles, and polygons given their attributes.

·  6.93  Determine the congruence of segments, angles, and polygons given their properties.

·  6.94  Determine whether polygons are congruent or noncongruent according to the measures of their sides and angles.

6.123  Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate.  Apply these techniques in the context of solving practical and mathematical problems.

·  6.92  Draw lines of symmetry to divide regular polygons into two congruent parts.

### KEY VOCABULARY

congruent, non-congruent, polygon, corresponding sides, construct, line segments, angles, inferences, coordinate plane, vertices, faces, edges, angles, attributes

Updated: Oct 27, 2017