Download Geometry Fall 2016 Lesson 018 _SAS Postulate

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Lesson Plan #18
Date: Monday October 24th, 2016
Class: Geometry
Topic: Proving triangles congruent by the S.A.S postulate
HW #18:
Read pages 117-118, page 120 #’s 1, 4, 7, 10
Page 123 #’s 1-3
Aim: How do we prove triangles congruent by the S.A.S postulate?
Objectives:
1) Students will be able to define congruent polygons.
2) Students will be able to define corresponding parts of congruent polygons
3) Students will be able to understand the S.A.S. postulate.
4) Students will be able to use the S.A.S. postulate to prove triangles congruent.
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Note: Test on Friday
October 28th.
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Do Now: At right are two polygons (what type? _____________) where one can be moved in such a way that the
sides and angles of one polygon fit exactly upon the sides and angles of the second polygon. How do we classify these
two polygons?
PROCEDURE:
Write the Aim and Do
Now
Get students working!
Take attendance
Give Back HW
Collect HW
Go over the Do Now
In geometry, two sets of points are called congruent if, and only if, one can be transformed
into the other by an isometry, i.e., a combination of rigid motions, namely a translation, a
rotation, and a reflection. This means that either object can be repositioned and reflected (but
not resized) so as to coincide precisely with the other object.
http://www.mathsisfun.com/geometry/congruent.html
http://www.mathopenref.com/congruentpolygons.html
In the congruent polygons,
what vertex in the 2nd polygon corresponds to vertex A in the first polygon?
Name the other corresponding vertices
Name the corresponding sides
Definition: Two polygons are congruent if their vertices can be matched up so that the corresponding sides and angles (or
corresponding parts for short) of the polygons are congruent.
Online Activity:
Let’s mark the corresponding parts in the congruent triangles below.
Indicate the corresponding parts of the
congruent triangles at right
Online activity:
http://www.mathopenref.com/congruenttriangles.html
Examine the two triangles at left with the indicated sides and angles congruent.
What do you notice about the two triangles?
Let’s explore pairs of triangles that have two corresponding sides congruent and the included angle congruent
http://www.mathopenref.com/congruentsas.html
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Postulate: Two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and
the included angle of the other [s.a.s.] [s.a.s.]
Online Activity: http://www.glencoe.com/sites/texas/student/mathematics/assets/animation/geometry/GEOCIM4-4.swf
Follow along with a piece of scrap paper.
Assignment #1: How many different (size) triangles can you construct using the two sides and the included angle below?
Assignment #2:
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Example #1:
Statements
Reasons
Example #2:
Statements
Reasons
On Your Own: Complete the 3 proofs below: Do the proofs on a separate sheet of graph paper.
14. Determine if the pair of triangles are congruent. If they
are, state the rigid motions that would justify the triangles
being congruent. Then state the congruence postulate that
would show the triangles are congruent.
Rigid Motion:
Congruence Postulate:
Final Summary:
Side Angle Side - (SAS)
If there is a correspondence between two sides and the included angle of two triangles,
such that corresponding sides are congruent and the corresponding included angles are
congruent, then the triangles must be congruent.
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If Enough Time:
Statements
Reasons
Statements
Reasons
Statements
Reasons
Statements
Reasons