4.2 Apply Congruence and Triangles
Goal  Identify congruent figures.
Day 1:
Read pg 225 and write the definitions for the given vocabulary words.
VOCABULARY
Congruent figures
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Corresponding parts
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Example 1
Identify congruent parts
Write a congruence statement for the triangles. Identify all pairs of congruent corresponding parts.
Corresponding angles A  _____, B  _____, C  _____
Corresponding sides AB  ____, BC  ____, CA  _____
Watch Burger video 4.3 examples 1 and 2.
Example 2
Use properties of congruent figures
In the diagram, QRST  WXYZ.
a. Find the value of x.
b. Find the value of y.
a. You know Q  W.
mQ  _______
65°  _________
_____  _____
_____  x
b. You know QR  WX .
QR = ______
6  _______
6  ________
____  y
Checkpoint In Exercises 1 and 2, use the diagram shown in which FGHJ  STUV.
1. Identify all pairs of congruent corresponding parts.
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2. Find the value of x and find mG.
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Example 3
Show that figures are congruent
Maps: If you cut the rectangular map in half alongPR , will the sections of the map be the same size and
shape? Explain.
Solution
From the diagram, S  _____ because all right angles are congruent. Also, by the Lines Perpendicular to a
Transversal Theorem,
PQ || _____ . Then l  _____ and 2  _____ by the
_______________________________. So, all pairs of corresponding angles are _______________ .
The diagram shows PQ  ____ and QR  _____ . By the ________________ ,PR  RP. All corresponding
parts are ______________ _, so PQR  __________. _________, the two sections will be the same
_________ and __________.
PQ
RS
Day 2:
Read pgs. 226-228
THEOREM 4.3: THIRD ANGLES THEOREM
If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also
_______________.
Example 4
Use the Third Angles Theorem
Find mV.
Solution
SUT  VUW by the ________________________________. The diagram shows that
STU  _________ , so by the Third Angles Theorem, S  _________. By the Triangle
Sum Theorem, mS = __________________ = _______. So, mS  mV = _______ by the definition of
congruent angles.
Example 5
Prove that triangles are congruent
Write a proof.
Given
Prove
FH  JH , FG  JG ,
FHG  JHG, FGH  JGH
FGH  JGH
Plan for Proof
a. Use the Reflexive Property to show ______________.
b. Use the Third Angles Theorem to show ____________.
Plain in Action
Statements
Reasons
1. FH  JH , FG  JG
_________
2. ___________
Reflexive Property of
Congruence
3. FHG  JHG,
___________
FGH  JG
4. __________
Third Angles Theorem
5. FGH  JGH
_________________
THEOREM 4.4: PROPERTIES OF CONGRUENT TRIANGLES
Reflexive Property of Congruent Triangles
For any triangle ABC, ABC  _________.
Symmetric Property of Congruent Triangles
If ABC  DEF, then ________________.
Transitive Property of Congruent Triangles
If ABC  DEF, and DEF  JKL, then _________________.
Checkpoint Complete the following exercises.
3. In the diagram atjhe right, E is the midpoint of AC and BD . Show that
ABE  CDE.
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4. In the diagram, what is the measure of D?
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5. By the definition of congruence, what additional information is needed to know that ABE  DCE in
Exercise 4?
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Homework
Day 1: pp. 228–231 Exs. 1–14, 36–40
Day 2: pp. 228–231 Exs. 15–21, 23–31, 33-35