Download File

Geometry CP
Unit 4: Congruency
of Triangles Outline
NOTE: Mr. Beegle reserves the right to amend, add to, or take away from
assessments, assignments, and/or activities on an as-needed basis.
NOTE: Expect pop quizzes, opensting tickets, and buzz tickets as well.
NOTE: Dates are subject to change.
DATE:
Lesson:
Assessment:
_______
4.1—Congruent Polygons
___________________________
_______
4.2—Triangle Congruence
___________________________
_______
4.3—Analyzing Triangle Congruence
___________________________
_______
4.4—Using Triangle Congruence
___________________________
_______
Unit 4 Test
___________________________
_______
Match.com Project
___________________________
Geometry CP
4.1—Congruent Polygons (pp. 210-213)
Upon completing this lesson, students will be able to:
1. Define congruent polygons.
2. Solve problems by using congruent polygons.
 Remember from previous lessons that is something is congruent, that it
________________________________________________________________________.
 Another way to look at it is that you could take any polygon and “slide”
it on top of the same polygon.
Naming Polygons
• Here we see a triangle.
• When naming a polygon, start at any point
on the figure, then go
______________________________________________________________________.
• Using this rule, we can name this triangle six different ways.
• ________________________________________________________________________.
Corresponding Sides and Angles
 Two polygons can be corresponding if they
______________________________________________________
_______________________________________________________
 Here we have quadrilaterals ADCB and EHGF.
 How can we prove that they are corresponding?
 Notice that when we named the triangle in the earlier side, we came up
with 6 different ways.
 Notice that when we named the quadrilateral in the last side, we came
up with 8 different ways.
 This lets us see a pattern in that ______________________________________________
___________________________________________________________________________________
in order to show the different ways that we can either name the polygon
or show correspondence.
Congruency Statements
 Whenever we write a congruency statement about two polygons, we
have to write the letters of the vertices in the proper order so that they
correspond.
 How would we write a congruency statement using these
quadrilaterals?
Polygon Congruence Postulate
 States that two polygons are congruent if and only if there is a
correspondence between their sides and angles such that:
 ___________________________________________________________________________________
 ___________________________________________________________________________________
 So if you remember from the previous slide, the number of ways to
prove congruency is twice the number of sides of the polygon.
Geometry CP
4.2—Triangle Congruence (pp. 217-220)
Upon completing this lesson, students will be able to:
1. Explore triangle rigidity.
2. Develop congruence postulates for triangles (SSS, SAS, and ASA)
 There are many different ways to determine that a triangle and
congruent.
 Almost all of them involve either angles or sides.
SSS Postulate
 ___________________________________________________________________________________
 ___________________________________________________________________________________
___________________________________________________________________________________
SAS Postulate
 ___________________________________________________________________________________
 ___________________________________________________________________________________
___________________________________________________________________________________
ASA Postulate
 ___________________________________________________________________________________
 ___________________________________________________________________________________
___________________________________________________________________________________
Geometry CP
4.3—Analyzing Triangle Congruence (pp. 226-229)
Upon completing this lesson, students will be able to:
1. Identify and use the SSS, SAS, and ASA Congruence Postulates and the AAS
and HL Congruence Theorems.
2. Use counterexamples to prove that other side and angle combinations
cannot be used to prove triangle congruence.
AAA Postulate?
 Angle-Angle-Angle?
 In looking at the triangles on the next slide,
what can we prove? What do we need to
prove congruency?
 So as we saw from the previous slide, we proved they were congruent
through their angles, but not necessarily their sides.
 Thus, AAA is not a way to prove congruency.
AAS Theorem
 ___________________________________________________________________________________
 ___________________________________________________________________________________
___________________________________________________________________________________
Difference between AAS and ASA
 AAS is a ___________________________, ASA is a __________________________________.
 With AAS, the congruent parts must correspond.
HL Theorem
 ___________________________________________________________________________________
 ___________________________________________________________________________________
___________________________________________________________________________________
 What makes the HL Theorem different from the other postulates and
theorems we’ve looked at?
Geometry CP
4.4—Using Triangle Congruence (pp. 245-249)
Upon completing this lesson, students will be able to:
1. Use congruence of triangles to conclude congruence of corresponding
parts.
2. Develop and use the Isosceles Triangle Theorem
 Go back to the triangles in the previous slide.
 How many ways can we prove the triangles congruent
 Name them.
 If you can prove that all sides of a triangle are congruent and that all
angles of a triangle are congruent, you can use CPCTC
___________________________________________________________________________________
 You only use CPCTC after determining ___________________________ way that
two sets of triangles are congruent.
 In order to properly use CPCTC in context, we can use a
__________________________________________________.
 Given: Two segments, MP and NQ, bisect each other at Point O
 Prove: MN ≅ PQ
Isosceles Triangle
 Isosceles triangles have at least ______________________ congruent sides.
 Made up of two ______________________ and a ______________________.
 The angles opposite the legs are ____________________________________________.
 The angle opposite the base is the _________________________________________.
Isosceles Triangle Theorem
 ___________________________________________________________________________________
___________________________________________________________________________________
Corollary
 Corollaries are ______________________________________________ that can be
derived from original theorems.
 Two common ones are:
The measure of each angle of an equilateral triangle is 60°
The bisector of the vertex angle of an isosceles triangle is the
perpendicular bisector of the base.