Name: ___________________________ Block:______
Chapter 4 – Congruent Triangles
Date
Assignment
Score
Learning
Target(s)
Notes
What am I confident about?
Where do I need to spend more time?
Am I weak on a prerequisite skill?
Learning Targets:
Classify triangles and find measures of their angles.
Identify congruent figures.
Use theorems about isosceles and equilateral triangles.
Use the side lengths to prove triangles are congruent.
Use sides and angles to prove congruence.
Use two more methods to prove congruence.
Use congruent triangles to prove corresponding parts congruent.
1
Unit 4 Syllabus: Ch. 4 Congruent Triangles
Block Date
Topic
3
Homework
B 11/11
A 11/12
B 11/13
A 11/14
4.1 Classifying Triangles
B 11/17
A 11/18
B 11/19
A 11/20
4.1, 4.2, and 4.7 Quiz
Worksheet: 4.1 Identifying
Triangles
Worksheet: 4.2 Congruent
Triangles and 4.7 Isosceles
and Equilateral Triangles
Khan Academy
4.3 – 4.5 Congruent Triangle Proofs
Day 1
Worksheet: 4.3-4.5 Proving
Triangles Congruent
7
B 11/21
A 11/24
Worksheet: 4.3-4.5 Review
8
B 11/25
4.3 – 4.5 Congruent Triangle Proofs
Day 2
Open Note Quiz
4.6 CPCTC Proofs
4
5
6
4.2 Congruent Triangles
4.7 Isosceles and Equilateral Triangles
Worksheet: 4.6 CPCTC
Thanksgiving Break
8
9
A 12/1
4.6 CPCTC Poofs
Worksheet: 4.6 CPCTC
B 12/2
Review Day Ch 4
Review Worksheet
A 12/3
10
B 12/4
Ch 4 Test
Khan Academy
A 12/5
***Syllabus subject to change due to weather, pep rallies, illness, etc
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and Monday, Wednesday, and Thursday afternoons.
2
Name: ___________________________________Block: _______
HW: 4.1 Identifying Triangles
Date: ___________
18
Match the triangle description with the most specific name. (1 point each)
_____
_____
_____
_____
_____
_____
7. Can a right triangle also be obtuse? Explain why or why not. (2 points)
8. A triangle has the given vertices. Graph the triangle and classify it by its sides. Then determine if
it is a right triangle.
A (3, 3), B (6, 9) , C (6, -3) (2 points)
3
For questions 9 and 10, find the value of x. Then classify the triangle by is angles (2 points)
9.
10.
x=
Triangle: ___________
x=
Triangle:
11. Find the measure of the exterior angle (2 points).
#12-17 Find the measure of the numbered angle. (1 point each)
12. m  1=
13. m  2 =
14. m  3 =
15. m  4 =
16. m  5 =
17. m  6 =
18. Find the values of x and y. (2 points)
x=
y=
4
HW: 4.2 Congruent Triangles and 4.7 Isosceles and Equilateral Triangles
In the diagram, MLK  JTE . Complete the statement.
1.
2.
28
4.
5.
7. Find the value of x.
8. Identify all pairs of congruent corresponding
parts when ABC  DEF
9. Suppose ABC  EFD , EFD  GIH ,
m  A = 90, and m  F = 20. What is m  H?
Complete the statement.
Tell what theorem you used.
10.
11.
12.
13.
Find the unknown measure.
14.
AB = ______
15.
ML= _______
16.
m<T = _______
5
Find the value of x and y.
17.
18.
x = ______
19.
x = _____
20.
x = ______
21.
x = _____ y = ______
22.
x = _____ y = ______
x = _____ y = _____
Identify each figure as congruent or not congruent. For those that can be proven congruent, WRITE A CONGRUENCE
STATEMENT.
23.
26.
24.
25.
27.
28
6
HW: 4.3-4.5 Proving Triangles Congruent
23
Select the method which will prove the triangles congruent, if possible.
SSS Postulate
SAS Postulate
______________
AAS Theorem
______________
______________
8.
ASA Postulate
HL Theorem
______________
______________
A
______________
______________
P
9. A
P
None
10.
60
61
C
C
B
Q
ABC  _______ by ________
11.
B
B
Q
ABC  _______ by _______
G
59
60
ABC  _______ by _______
A
A
A
12.
13.
B
V
B
C
C
C
D
ABC  _______ by ________
S
U
T
ABC  _______ by _______
ABC  _______ by _______
7
Name the included angle between the pairs of sides.
14. MT and TR
15. RT and QR
16. MR and TM
State the 3rd congruence that much be given to prove that
17. Given:  A   X
B  Y
Method: AAS Theorem
18. Given:  A   X
AB  XY
Method: ASA Theorem
ABC  XYZ .
19. Given:  C   Z
BC  YZ
Method: AAS Theorem
Use the given coordinates to determine if  ABC DEF. (*Hint- distance formula or graph)
20. A ( 2, -2) B (5, 1) C (4, 8)
D (7, 5) E (10, 8) F (9, 13)
21. A ( 1, -1) B (-2, 2) C (-3, -4)
D (3, 2) E (6, -1) F (7, 5)
Tell whether you can use the given information to determine whether JMR  XZY .
22. JM  XZ , M  Z , R  Y
23. JM  XZ , JR  XY , J  X
8
HW: 4.3-4.5 Review
Directions: Complete all of the problems and show all work if necessary.
24
Determine which method you would use to prove the two triangles congruent. If none of the methods apply,
write NONE.
1. __________________
2. ____________________
3.__________________
4. __________________
5. ____________________
6.__________________
For the following, mark the congruent parts in the triangles DEF and RST. If the
triangles can be proved congruent by the method given, what additional parts are
needed?
9
13.
14.
Statements
Reasons
1. BE  BC
1._______________
2. A  D
2._______________
3. ABE  CBD
3._______________
4. ABE  DBC
4._______________
10
HW: 4.6 CPCTC
38
1) Complete the proof (1 point per line)
Statements
1.
Reasons
1.
2.
2.
3.
3.
4.
4.
2) Complete the proof (2 point per line)
Given: BD
AD  CD
3  4
Prove: 5  6
Statements
Reasons
1. Given
1.
2.
3.
4.
5.
6.
2. Two angles that form a linear pair are
supplementary.
3. Supplements of the same angle, or congruent
angles, are congruent.
4.
5.
6.
11
3.) Complete the proof (2 point per line)
Statements
Reasons
1.
1.
2.
2.
3.
3. Right angles are congruent.
4.
4.
5.
5.
4.) Complete the proof (2 points per line)
Statements
1.
2.
3.
;
Reasons
1. Given
2.
3.
4.
4.
5.
5.
6.
7.
6.
7. If two sides of a triangle are congruent, the
angles opposite them are congruent.
12
HW: Review Ch 4
27
Basic Triangle Information
1.) Given the diagram, identify the following triangles.
a.) right scalene triangle
__________
b.) equiangular triangle
__________
c.) obtuse isosceles triangle.
__________
2.) Given the diagram, identify the following terms.
a.) In ABD, identify the vertex angle. _______
b.) In ACD, identify the hypotenuse. _______
c.) In ACD, identify the legs. _______, _______
d.) In ABD, identify the legs. _______, _______
3.) Complete the sentence with always, sometimes, or never.
a.) An isosceles triangle is _________________ a right triangle.
b.) An obtuse triangle is _________________ a right triangle.
c.) An isosceles triangle is _________________ an equilateral triangle.
d.) An obtuse triangle is _________________ an isosceles triangle.
Solve for the variables
4.) x = _____
6.) x = _______
5.) x= _______
7.) x = _______
y = _______
13
8.) x = _______; y = _______
10.) x = _______
9.) x = _______
11.) x = _______
12.) Solve for the missing angles.
m1 = _____ m2 = _____
m3 = _____
In each diagram, the given triangles are congruent. Solve for the variable.
13.) x = _______
14.) x = _______
14
Solve for each variable. Show all work.
15.) x = _______
17.) x = _______; y = _______
16.) x = _______; y = _______
18.) x = _______
19.) What is the perimeter of the triangle?
___________
15
Determine if the triangles are congruent. If so, state the postulate.
20.) ______________
23.) ______________
21.) ______________
24.) ______________
22.) ______________
25.) ______________
Complete the proof.
26.
27.
A  C
Statements
Reasons
16