Geometry, Teacher\'s Edition

(^6) L, (^6) C∼= (^6) P, and so forth.
Stress the tic mark notation in relation to the congruency statement. Simply because the letters used are in alphabet-
ical order does not necessarily mean they will line up this way in a congruency statement. Students must follow the
tic marks around the figure when writing congruency statements.
Look Out!Students begin to become confused with notation at this point. Be consistent with notation. Have groups
of students create classroom posters regarding symbols.
Use the following mantra, “Distances are equal and side lengths are congruent.” While each lends to the other,
students need to understand which value applies.
Ask students to determine if the below triangles are congruent and explain any reasoning. Use the following
information:DE∼=ABandEF∼=BC.These are not congruent because the double tick marks do not match.
Proof Using SSS
Pacing:This lesson should take one class period
Goal: This lesson introduces students to the formal concept of triangle congruency. The easiest for students to
visualize is the side-side-side (SSS) Congruence Postulate.
Differentiation!For students struggling with the distance formula, encourage them to create a right triangle using
theriserunof the line. Then students can use Pythagorean’s Theorem leg^2 +leg^2 =hypotenuse^2 to find the length of the
segment.
Arts and Crafts Time! Students can visualize the SSS Congruence Postulate in the following way. Using three
8. 5 [U+0080][U+009D]× 11 [U+0080][U+009D]sheets of paper, have students create three dowels by rolling tightly
from corner to opposite corner. Cut the dowels to the following lengths: 4[U+0080][U+009D], 6 [U+0080][U+009D],
and 7.[U+0080][U+009D]Using tape, glue, or staples, the students should create a triangle and compare their figure
with the figures of several classmates.Students should see that all triangles are congruent, helping to demonstrate
the rationale behind the SSS Congruence Postulate.
Background Information!The SSS Congruence Postulate can be proved using the idea of congruence. In theory, as
mentioned in the lesson, these two triangles represent a slide of 7 units right and 8 units down. A slide, ortranslation,
is an isometry, preserving distance and angle measure. Thus, since the distances are equal, the lengths are congruent.
1.4. Congruent Triangles