Download Chapter 4

Answers
1. yes 2. no 3. yes 4. no 5. yes
1. m<A = 45; m<B =45; m<C=90
right isosceles
2. m<K =80; m<L = 60; m<M = 40;acute
scalene
3. 120
Chapter 4
Congruent Triangles
Agenda and Objectives
Agenda
Notes, practice, review 4-1
 Notes, practice, review 4-2

Objectives
Identify congruent figures and
corresponding parts
 Prove that two triangles are congruent
 Prove that triangles are congruent using
the SSS and SAS Congruence Postulates

Section 4-1 Congruent Figures
Review:
 What
makes angles

?
same degree measurement
 What
makes segments
same length

?
Can an angle be congruent to
a segment?
Can a triangle be congruent to
a square?
What makes figures congruent?
Congruent Figures
Two figures that have the
same size and shape.
If figures are congruent then
they have congruent angles
and congruent sides or parts.
Let’s Take a Look
Corresponding
Angles
Corresponding
Sides
Labeling Congruent Figures
Congruent figures
must be labeled
according to their
corresponding parts.
Ex: Label the following congruent figures.
Possible Answers
Δ1  Δ2
Δ ABC  Δ EFD
Δ BCA  Δ FDE
Δ CBA  Δ DFE
Δ2
Δ EFD
Δ FDE
Δ DEF
Δ1
Δ ABC
Δ BCA
Δ CAB
 Δ3
 Δ HGI
 Δ GHI
 Δ IHG
 Δ3
 Δ HGI
 Δ GIH
 Δ IHG
Ex: Given: Δ CAT  Δ DOG
Which angles are congruent to one another?
C
and D
 A and O
 T and G
Which sides are congruent to one another?
 CA
and DO; AC and OD
 AT and OG; TA and GO
 TC and GD; CT and DG
To help solve, draw a picture!
You try..
Page 119 1-9, 12-17
Please work independently
Answers
1.
2.
3.
4.
5.
6.
7.
8.
9.
FI, WE; IN, EB; FN, WB
∠ F, ∠ W; ∠ I, ∠ E; ∠ N, ∠ B
YES
NO
∆CDO
∠C
CO
DO
Yes because AO = OC and DO = OB
Answers continued
12. R
13. ROHES
14. m ∠C
15. 4
16. ∠
A
17. The leaf in the lower left hand corner is
flipped over.
Applications to Proofs
When the definition of congruent
triangles is used in a proof we write,
Corr. parts of  Δ’s are 
or CPCTC !!!
Current Goal:Identify/label
CPCT.
Future Goal: Use  parts
to prove that figures are 
and vice versa.
Example
The two triangles shown are congruent.
Complete…
∆STO ≅ ________
 ∠S ≅ ____ because ____.
 SO ≅ ___ because ____.
 Then point O is the midpoint of ____.
 ∠T ≅ ___ because ___.
 Then ST || RK because ____.

Practice: Classwork
Worksheet SKIP #3
Complete and we will go over.
Closure to 4.1
1.
2.
3.
4.
5.
On a little piece of paper write never, sometimes or
always.
An acute triangle is ____ congruent to an obtuse
triangle.
A polygon is ____ congruent to itself.
A right triangle is _____ congruent to another right
triangle.
If ∆ABC ≅ ∆XYZ, ∠A is ____ congruent to ∠Y.
If ∆ABC ≅ ∆XYZ, ∠B is ____ congruent to ∠Y.
Homework
page 120
Written Exercises #1-11 (SKIP 10) & #14