Download Unit 4 Notes Packet 2 PA 2014-15

Name:
Unit 4: Triangles
Period:
Date:
Notes Packet #2: Section 4.3/4.4/4.5: Triangle Congruence (PA)
CRS
CCSS
Review:
PPF 24-27 Use several angle properties to find an unknown angle
measure
G-CO. 8 Use the definition of congruence in terms of rigid motions to show
that two triangles are congruent if and only if corresponding pairs of sides and
corresponding pairs of angles are congruent.
EEI 20-23 Evaluate algebraic expressions by substituting integers
for unknown
Focus
PPF: 28-32 Apply properties of 30°-60°-90°,45°-45°-90°, similar,
and congruent triangles
G-SRT.5 Use congruence and similarity criteria for triangles to solve problems
and to prove relationships in geometric figures.
Extension:
PPF: 28-32 Apply properties of30°-60°-90°,45°-45°-90°, similar,
and congruent triangles
PPF 33-36 Draw conclusions based on a set of conditions
Solve multistep geometry problems that involve integrating
concepts, planning, visualization, and/or making connections
with other content areas
Level 1 Objectives
Name congruent triangles based on information provided (use CPCTC).
Name and label corresponding congruent parts of congruent triangles.
Set up and solve equations using congruent triangles.
“Basic” Definition Congruent Triangles
Definition of Congruent Triangles (CPCTC)
Naming  corresponding parts of  triangles
a) Name the congruent angles and sides for the following two triangles.
Angles:________________ Sides:________________
________________
________________
________________
________________
Congruence Triangles:
▲ __________  ▲__________
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b)
A  ______
B ______
F ______
AC  ______
DE  ______
FE  ______
c) ∆ABD  ∆CBD. Name the congruent angles and sides
Identify the congruent triangles in each figure and name the corresponding congruent parts:
1.
2.
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3. If ▲ABC  ▲DEC, name all corresponding sides and angles.
Algebra Crossover:
1. ∆GHI ≅ ∆ RST, HI =14, GH = 12, GI = 10, and ST = 2x + 4.
a. Draw and label a figure to show the congruent triangles.
b. Find x
2. ∆ABC≅ ∆DEF, mA = 40°, mE = 60°, mF = (4x -20)
a. Draw and label a figure to show the congruent triangles.
b. Find x
Homework Level 1
Page 195 #2-5,9-16,29-32
Congruence and Triangles Worksheet
CPCTC Worksheet
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Level 2 Objectives
Recognize when triangles are congruent by Side-Side-Side and Side-Angle-Side postulates.
Properties of Equality for Segments and Angles
Segments
Reflexive Property
AB = AB
Symmetric Property
If AB = CD, then CD = AB
Transitive Property
If AB = CD and CD = EF,
then AB = EF
Angles
Remember:
A postulate is a statement that is accepted as true without proof
Ex. Through any two points, there is exactly one line.
A theorem is a statement that has been proven true.
Ex. Linear Pair Theorem: Linear pairs are supplementary.
Proving Triangles Congruent by SSS and SAS
Directions: Determine which postulate, if any, can be used to prove that the two triangles are congruent. If the triangles
cannot be shown to be congruent, write “cannot be determined.”
1.
2.
4.
5.
3.
6.
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Directions: Complete each statement and tell which congruence shortcut you used to determine that the triangles are
congruent. If the triangles cannot be shown to be congruent, write “cannot be determined.”
2)
3)
▲ABC  ▲________
▲EF G ▲________
Reason: _________
Reason: _________
▲NPR  ▲________
Reason: _________
Homework Level 2
SSS and SAS Congruence Worksheet
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Level 3 Objectives
Recognize when triangles are congruent by Angle-Side-Angle and Angle-Angle-Side postulates.
Proving Triangles Congruent by ASA and AAS
Directions: Determine which postulate, if any, can be used to prove that the two triangles are congruent. If the triangles
cannot be shown to be congruent, write “cannot be determined.”
1)
2)
3)
Directions: Complete each statement and tell which congruence shortcut you used to determine that the triangles are
congruent. If the triangles cannot be shown to be congruent, write “cannot be determined.”
1)
▲STV  ▲________
Reason: _________
2)
3)
▲WXY ▲________
Reason: _________
▲STU  ▲________
Reason: _________
Homework Level 3
ASA and AAS Congruence Worksheet
Triangle Congruence Postulate Worksheet
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Level 4 Objectives
Combine all congruence postulates including CPCTC to prove two triangles are congruent.
Using the SSS, SAS, AAS, ASA and CPCTC
1) GIVEN: D is the midpoint of both GE and FH.
PROVE: ▲FDE  ▲HDG.
What are the three congruent parts?
Why are they congruent?
____________________________ because ____________________________________________
____________________________ because ____________________________________________
____________________________ because ____________________________________________
What is the reason ▲FDE  ▲HDG? ________________
2) GIVEN: BD bisects AC at D and AB  CB.
PROVE: ▲ABC  ▲CBD
What are the three congruent parts?
Why are they congruent?
____________________________ because ____________________________________________
____________________________ because ____________________________________________
____________________________ because ____________________________________________
What is the reason ▲ABC  ▲CBD? ________________
By proving that two triangles are congruent, you can deduce information about the other three parts. As you know a
triangle has six basic parts and we have to get three parts of one equal to three parts of the other (the right three parts) in
order for them to be congruent. This means we get the remaining three parts as a bonus because when figures are
congruent all the parts of one are equal the corresponding parts to the other. The other three parts are equal for the
reason: Corresponding Parts of Congruent Triangles are Congruent (CPCTC).
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3) GIVEN: N is the midpoint of AB
AX  NY
NX  BY
PROVE: X  Y
What are the three congruent parts?
Why are they congruent?
____________________________ because ____________________________________________
____________________________ because ____________________________________________
____________________________ because ____________________________________________
▲ _________  ▲ __________ because of __________
X  Y because______________
4) GIVEN: VB bisects EVO
BV bisects EBO
PROVE:   BO
What are the three congruent parts?
Why are they congruent?
____________________________ because ____________________________________________
____________________________ because ____________________________________________
____________________________ because ____________________________________________
▲ _________  ▲ __________ because of __________
  BO because______________
Level 4 Homework
Triangle Congruence Proof Worksheet
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