4.1 apply congruence and triangles 4.2 prove triangles congruent by sss, sas objectives: 1. to...
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4.1 Apply Congruence and Triangles4.2 Prove Triangles Congruent by SSS, SAS
Objectives:1. To define congruent triangles2. To write a congruent statement3. To prove triangles congruent by SSS,
SAS
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Congruent Polygons
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Congruent Triangles (CPCTC)
Two triangles are congruent congruent triangles triangles if and only if the ccorresponding pparts of those ccongruent ttriangles are ccongruent.
• Corresponding sides are congruent
• Corresponding angles are congruent
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Congruence Statement
When naming two congruent triangles, order is very important.
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Example
Write a congruence statement for the congruent triangles below.
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Example
Which polygon is congruent to ABCDE?ABCDE -?-
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Properties of Congruent Triangles
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Example
What is the relationship between C and F?
30
30
75
75
E
F
D
A
C
B
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Third Angle Theorem
If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.
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Congruent Triangles
Checking to see if 3 pairs of corresponding sides are congruent and then to see if 3 pairs of corresponding angles are congruent makes a total of SIX pairs of things, which is a lot! Surely there’s a shorter way!
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Congruence Shortcuts?
Will one pair of congruent sides be sufficient? One pair of angles?
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Congruence Shortcuts?
Will two congruent parts be sufficient?
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Congruent Shortcuts?
Will three congruent parts be sufficient?
And if so….what three parts?
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Investigation…
… Using 2,3,4 Triangles
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Side-Side-Side Congruence Postulate
SSS Congruence Postulate:SSS Congruence Postulate:If the three sides of one triangle are
congruent to the three sides of another triangle, then the two triangles are congruent.
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SSS Congruence Postulate
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A B
C
D
Using a 2-Column Proof!
Is ABC is congruent to ABD? Why or why not?
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Example
Decide whether the triangles are congruent. Explain your reasoning.
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Investigation…
…
Part 2
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Congruence Shortcuts
Side-Angle-Side (SAS) Congruence Side-Angle-Side (SAS) Congruence Postulate:Postulate:
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
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Can we prove?...yet?
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What else would we need?
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Can we Prove Triangle Congruence?
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Another Proof…?
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Classwork
From 4.13 - 1232 – 3538 – 4046 – 48*
From 4.21 - 48 - 1722 - 3041 - 42