Download unit #6: triangle congruence

Name _________________________________________
Period ____
10/24 – 11/3 Pre-AP
UNIT #6: TRIANGLE CONGRUENCE
I can define, identify and illustrate the following terms
congruent polygons
obtuse triangle
equilateral triangle
exterior angle
equiangular triangle
scalene triangle
right triangle
acute triangle
interior angle
auxiliary lines
isosceles triangle
SSS
SAS
AAS
HL
ASA
Dates, assignments, and quizzes subject to change without advance notice
Monday
24
Classifying and Angle
Relationships
31
CPCTC
Tuesday
25
Isosceles, Equilaterals,
and Congruent
Polygons
1
Review
Block Day
26/27
Congruent Triangles
(with basic proofs)
Friday
28
Proofs
QUIZ
2/3
TEST
Monday, 10/24
Classifying Triangles (4-1) and
Angle Relationships in Triangles (4-2)
Check Point
Grade:
2) I can classify triangles by sides and angles
3) I can use triangle classifications to find angle measures and side lengths.
4) I can use triangle sum theorem to solve missing angles of a triangle
5) I can use exterior angle theorem to find missing angles of a triangle
Grade:
ASSIGNMENT: pg 219 #13-19 odd, 24-34 even 35-37 all (13
Test
/41
=
%
/6
/12
problems)
pg. 223 #17-21, 23, 29-34, 44, 45
(14 problems)
Tuesday, 10/25
Congruent Polygons (4-3) and
Triangle Properties (4-8)
Check Point
Grade:
6) I can use the properties of equilateral triangles to find missing side lengths and
angles
Test
/17
=
%
/9
7) I can write a congruency statement representing two congruent polygons
8) I can identify congruent parts of a polygon, given a congruency statement
9) I can find the side lengths and angle measures using properties of congruent polygons
10) I can use the properties of isosceles triangles to find missing side lengths and
angles
ASSIGNMENT: pg. 277 #13-19 odd, 22-26, 28, 29, 33, 34 (13
Grade:
problems)
pg. 235 #19, 23-25, 30-36 (11 problems)
/8
Wednesday and Thursday, 10/26-27
Determine if Triangles are Congruent (4-4 and 4-5)
Check Point
Draw and describe the five ways to
Grade:
show that two triangles are congruent.
11) I can name the five ways to prove triangles are congruent
12) I can determine whether triangles are congruent
13) I can prove triangles are congruent using SSS, ASA, AAS, SAS, HL.
14) I can mark pieces of a triangle congruent given how they are to be proved congruent.
ASSIGNMENT: Triangle Congruence Worksheet
Grade:
Test
/54
=
%
Tested below
/36
/8
/10
Friday, 10/28
Proofs
Check Point
Grade:
15) I can write a two-column proof to show that two triangles are congruent.
ASSIGNMENT: Proofs Worksheet
Test
/41
=
%
/6
Grade:
Monday, 10/31
Triangle Proofs with CPCTC
Check Point
How many corresponding parts should be listed in your
Grade:
proof before you can conclude triangles are congruent?
15) I can write a two-column proof to show that two triangles are congruent.
ASSIGNMENT: Triangle Proofs Worksheet
Grade:
Test
/12
=
%
/12
Tuesday 11/1
Review
I can assess my knowledge and prepare for the test.
ASSIGNMENT: Review Worksheet
Grade:
Wednesday and Thursday, 11/2-3
Test 7 –Triangle Congruence
I can demonstrate knowledge skills, and reasoning ability of ALL previously learned material.
ASSIGNMENT: Test #7
Test
Grade:
Name __________________________ Period ______
Triangle Congruence
GH
I. For each pair of triangles, tell which postulate can be used to prove the triangles congruent.
1. ∆AEB ≅ ∆DEC
______________
2. ∆CDE ≅ ∆ABF ______________
A
D
E
C
F
C
B
E
A
B
D
3. ∆DEA ≅ ∆BEC
A
______________
4. ∆AGE ≅ ∆CDF ______________
B
E
D
C
5. ∆RTS ≅ ∆CBA
______________
6. ∆ABC ≅ ∆ADC ______________
B
T
S
C
A
C
R
A
7. ∆BAP ≅ ∆BCP
Given: BD bisects
B
______________
ABC
D
8. ∆SAT ≅ ∆SAR ______________
A
R
S
A
B
D
P
T
C
II. For each pair of triangles, tell: (a) Are they congruent (b) Write the triangle congruency statement.
(c) Give the postulate that makes them congruent.
1.
D
2.
C
3. Given: T is the midpoint of WR
O
A
E
T
E
L
A
E
R
W
V
B
a. ______________
a. ______________
a. ______________
b. ∆_____ ≅ ∆ _____
b. ∆_____ ≅ ∆ _____
b. ∆_____ ≅ ∆ _____
c. ______________
c. ______________
c. ______________
4.
5. Given: IH Bisects WIS
6.
I
W
H
S
L
U
G
E
a. ______________
a. ______________
a. ______________
b. ∆_____ ≅ ∆ _____
b. ∆_____ ≅ ∆ _____
b. ∆_____ ≅ ∆ _____
c. ______________
c. ______________
c. ______________
7.
8.
9.
H
P
A
T
M
a. ______________
a. ______________
a. ______________
b. ∆_____ ≅ ∆ _____
b. ∆_____ ≅ ∆ _____
b. ∆_____ ≅ ∆ _____
c. ______________
c. ______________
c. ______________
10. Given: I is the midpoint
of ME and SL
M
11.
12.
C
F
L
I
S
E
B
A
D
E
a. ______________
a. ______________
a. ______________
b. ∆_____ ≅ ∆ _____
b. ∆_____ ≅ ∆ _____
b. ∆_____ ≅ ∆ _____
c. ______________
c. ______________
c. ______________
III. Using the given postulate, tell which parts of the pair of triangles should be shown congruent.
1. SAS
2. ASA
3. SSS
C
A
E
D
B
F
F
B
A
B
A
E
D
C
C
D
_______ ≅ ________
4. AAS
________ ≅ ________
5. HL
_______ ≅ _______
6. ASA
P
P
D
S
C
T
R
A
Q
_______ ≅ ________
R
S
Q
________ ≅ ________
_______ ≅ _______
B
IV. For which value(s) of x are the triangles congruent?
1. x = _______________
2. x = _______________
D
D
5x - 8
F
E
B
A
5x° 92°
3x + 2
E
C
A
B
3. x = _______________
A
C
4. x = _______________
A
B
m ∠3 = x2
m ∠4 = 7x - 10
7x - 4
4x + 8
1
3
E
2
4
C
D
C
5. x = _______________
A
6. x = _______________
C
D
2
x + 3x
B
D
C
9x - 8
A
B
m ∠ CDB = (15x + 3)°
7. x = _______________
C
W
(2x + 4)°
A
m ∠ ABD = (10x + 18)°
8. x = _______________
D
1
B
R
2
Z
x2 + 2x
x2 + 24
(4x – 6)°
B
R
S
T
Name:
Period:
GH
Triangle Proofs Worksheet
For each problem below, write a two-column proof on a separate piece of paper.
I. Proving Triangles Congruent:
1.
5.
2.
3.
6.
4.
II. Using CPCTC
7.
10.
1
8.
9.
2
11.
Review: Triangles and Triangle Congruence
You will need a separate piece of paper to show all your work. This review is not comprehensive; always be sure
to go back through your old homework and quizzes.
C
I can write a congruency statement representing two congruent polygons
O
G
1. Write a congruency statement for the two triangles at right.
R
A
E
I can identify congruent parts of a polygon, given a congruency statement
2. List ALL of the congruent parts if EFG ≅ HGF
I can use algebra to find the side lengths and angle measures of congruent polygons
3. WXY ≅ZYX . Find p.
X
Y
2
2p
V
20
(7p+13
W
Z
4. ADC ≅CBA. Find x.
D
C
(2x 2 + 7)°
1
2
(x 2 – 8x)°
A
B
I can name the five ways to prove triangles are congruent
5.
Name the 5 ways to prove triangles congruent.
I can prove triangles are congruent
For each pair of triangles, tell: (a) Are they congruent (b) Write the triangle congruency statement. (c) Give
the postulate that makes them congruent.
B
6.
8. Given: I is the midpoint
of ME and SL
A
C
M
L
I
D
7.
S
A
E
T
W
R
E
I can mark pieces of a triangle congruent given how they are to be proved congruent
P
9. What information is
10.
What information is missing to use
missing to use HL?
SAS?
C
D
R
S
Q
A
B
I can use the exterior angle theorem and the triangle sum theorem to solve problems.
12. The measures of the angles of a triangle
11. Solve for x and find the measure of the
following angles.
G
are in the ratio of 1:4:7. What are the
measures of the angles?
OGE = ______
GEO = ______
EOM = ______
(x +16)o
(5x + 18)o
E
O (3x + 100)o
M
I can use the properties of isosceles and equilateral triangles to solve problems.
13. Draw and correctly mark the sides and angles of an equilateral, isosceles, and a scalene triangle.
14. Solve for x.
(-5x + 41)
(3x – 15)
15. The vertex angle of an isosceles triangle measures (6t – 9)° and one of its base angles measures (4t)°.
Find t.
I can write a two-column proof over congruent triangles
16.
17. Complete and review ALL proofs on the proofs worksheet.