# 7th Grade Module 6

New or Recently Introduced Terms

Correspondence (A correspondence between two triangles is a pairing of each vertex of one triangle

with one and only one vertex of the other triangle. A triangle correspondence also induces a

correspondence between the angles of the triangles and the sides of the triangles.)

Identical Triangles (Two triangles are said to be identical if there is a triangle correspondence that

pairs angles with angles of equal measure and sides with sides of equal length.)

Unique Triangle (A set of conditions for two triangles is said to determine a unique triangle if

whenever the conditions are satisfied, the triangles are identical.)

Three sides condition (Two triangles satisfy the three sides condition if there is a triangle

correspondence that pairs all three sides of one triangle with sides of equal length. The three sides

condition determines a unique triangle.)

Two angles and the included side condition (Two triangles satisfy the two angles and the included

side condition if there is a triangle correspondence that pairs two angles and the included side of one

triangle with angles of equal measure and a side of equal length. This condition determines a unique

triangle.)

Two angles and the side opposite a given angle condition (Two triangles satisfy the two angles and

the side opposite a given angle condition if there is a triangle correspondence that pairs two angles

and a side opposite one of the angles with angles of equal measure and a side of equal length. The

two angles and the side opposite a given angle condition determines a unique triangle.)

Two sides and the included angle condition (Two triangles satisfy the two sides and the included

angle condition if there is a triangle correspondence that pairs two sides and the included angle with

sides of equal length and an angle of equal measure. The two sides and the included angle condition

determines a unique triangle.)

Two sides and a non-included angle condition (Two triangles satisfy the two sides and a nonincluded

angle condition if there is a triangle correspondence that pairs two sides and a non-included

angle with sides of equal length and an angle of equal measure. The two sides and a non-included

angle condition determines a unique triangle if the non-included angle measures 90° or greater. If

the non-included angle is acute, the triangles are identical with one of two non-identical triangles.)

Right rectangular pyramid (Given a rectangular region ݐՠin a plane ݐج and a point ݑɠnot in ݐج the

rectangular pyramid with base ݐՠand vertex ݑɠis the union of all segments ݑɰݑàfor any point ݑàin ݐծ It

can be shown that the planar region defined by a side of the base ݐՠand the vertex ݑɠis a triangular

region, called a lateral face. If the vertex lies on the line perpendicular to the base at its center (the

intersection of the rectangle’s diagonals), the pyramid is called a right rectangular pyramid.)

Surface of a pyramid (The surface of a pyramid is the union of its base region and its lateral faces.)

Familiar Terms and Symbols

Vertical angles

Adjacent angles

Complementary Angles

Supplementary Angles

Angles on a line

Angles at a Point

Right rectangular prism

Suggested Tools and Representations

Familiar objects and pictures to begin discussions around cross sections, such as an apple, a car, a

couch, a cup, a guitar, etc.

A site on Annenberg Learner that illustrates cross sections

**Lesson 3**

protractor

**Lesson 6**

protractor

compass

ruler

**Lesson 7**

protractor

ruler

setsquare

**Lesson 8**

protractor

ruler

compass

or angle maker

**Lesson 9**

straws

paperclips

**Lesson 10**

parchment paper

**Lesson 11**

parchment paper

pasta

protractor

ruler

compass

**Lesson 16**

nets

solids

**Lesson 17**

nets

**Lesson 18**

nets

A site on Annenberg Learner that illustrates cross sections

**Lesson 19**

grid paper

**Lesson 21**

grid paper