Geometry, Teacher\'s Edition

English Connection!There are three main types of proofs: two-column, flow charts, and paragraph form. Use all
three methods when presenting this lesson (and subsequent lessons). Some students will be more comfortable with
organizing information in a 2-column format and others will use a flow chart. Students with a strong language arts
background will find that writing proofs using complete sentences in a paragraph will make the process of proving
similar to drafting a persuasive essay.

Homework Check!Using the bonus question following #10 is a great review for students regarding the appropriate
way to name angles. Be sure you review this question in class!

Proofs Using SAS and HL

Pacing:This lesson should take one class period

Goal: This lesson is to complete the triangle congruency postulates and theorems. There is a brief description
of the anatomy of a right triangle and Pythagorean’s Theorem. It also introduces the notion that AAA and SSA
relationships will not produce congruent triangles.

Note Taking Time!Students need help organizing these congruency proofs. Use a table similar to the one shown
below, projected on a digital imager or projector and take time to organize the material. Extend the organizer one
more column and two more rows to accommodate the information gathered in theUsing Congruent Triangles
lesson.

TABLE1.5:

Congruence Type Definition Diagram

SSS

SAS

ASA

AAS

HL

Extension!Use the following diagram from example 1 to further assess your students’ understanding of Triangle
Congruencies. Have students list the information needed for each of the four congruencies learned thus far: ASA,
SSS, SAS, and AAS.

1.4. Congruent Triangles