Chapter 4: Congruent Triangles

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Chapter 4 Congruent Triangles
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Section 4.1 Congruent Figures

• HW
• p.182 4,8,12,16,20,24,25,30,32,34,39

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Congruent Polygons
Two polygons are congruent if all of their
corresponding parts are congruent.
There are six corresponding parts in all. Can
you name them?
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Example
You must compare their corresponding parts. When
you name congruent polygons the letters must be
arranged in the same order to their corresponding
parts match up.
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Find the measure of angle A and angle B. Assuming
the triangles are congruent.
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First New Theorem

• If two angles of one triangle are congruent to
  two angles of another triangle, then the third
  angles are congruent.

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Proving triangles Congruent
Use the information given in the diagram. Give a
reason why each statement is true.
P
S
Q
R
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Section 4.2 Triangle congruence by sss and sas

• HW
• p. 189 2-16e, 22-30even, 33

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Triangle Congruence by SSS and SAS

• We know that for two triangles to be congruent,
  they have to have 3 congruent sides and 3
  congruent angles.
•  
• We dont always have to check all six parts.
  Sometimes it is enough to know 3 out of the 6
  things (depending on which 3 things it is.)

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Side-Side-Sides (SSS) Postulate
If the three sides of one triangle are congruent
to the three sides of another triangle, then the
two triangles are congruent.
To prove two triangles congruent by the SSS
postulate, the three pairs of sides need to be
congruent. If two triangles share a side, the
side is said to be congruent due to the reflexive
property.
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A Proof Using SSS
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Definitions
The word included is used frequently when
referring to the angles and the sides of a
triangle.
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Side-Angle-Side (SAS) 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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Examples
Which postulate (if any) could use to prove that
the two triangles are congruent?
1.
2. 3. 4.
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What other info, if any, do you need to prove the
two triangles are congruent by SSS or SAS?
1. 2.
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What other info, if any, do you need to prove the
two triangles are congruent by SSS or SAS?
1. 2.
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Section 4.3 Triangle congruence by asa and aas

• HW
• p.197 2-10all, 18 (Copy the whole Problem!),20-24e

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Section 4.4 Using Congruent triangles cpctc

• HW
• p. 205 1-4 7-12 (Write out complete proofs with
  drawings.) 14, 23

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Section 4.5 Isosceles and equilateral triangles

• HW
• p.213 1,3-16, 21-26

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Section 4.6 Congruence in right triangles

• HW
• p. 219 1-10, 16 and 17(Copy the whole problem),
  19, 20

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Section 4.7 Using corresponding Parts of
congruent triangles

• HW
• p. 226 1-3,4-8even, 12,14 (make a separate
  drawing for each problem) 28 (write out complete
  proof)