• ## EngageNY Resources

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
 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 