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Sec 1.4 CC Geometry – Parallel Lines and Angles Name: PARALLEL LINES
1. Give an alternate name for angle ∡ퟐ using 3 points: (1 answer)
2. Angles ∡푨푩푬 and ∡푪푩푮 can best be described as: (2 answers)
3. Angles ∡ퟔ and ∡ퟑ can best be described as: (2 answers)
4. The line 푮푯⃖ ⃗ can best be described as a: (1 answer)
5. Which angle corresponds to ∡푫푬푩 : (1 answer)
6. Angles ∡푭푬푩 and ∡푪푩푬 can best be described as: (2 answers)
7. Angles ∡ퟏ and ∡ퟖ can best be described as: (2 answers)
8. Which angle is an alternate interior angle with ∡푪푩푬 : (1 answer)
9. Angles ∡푮푩푪 and ∡푩푬푭 can best be described as: (2 answers)
10. Angles ∡ퟐ and ∡ퟖ can best be described as: (2 answers)
11. Which angle is an alternate exterior angle with ∡푨푩푮 : (1 answer)
12. Which angle is a vertical angle to ∡푨푩푮 : (1 answer)
13. Which angle can be described as consecutive exterior angle with ∡ퟏ : (1 answer)
14. Any two angles that sum to 180 ̊ can be described as angles. (1 answer)
p.17
M. Winking (Section 1-4)
● C
● A
● F
● D
These symbols imply the two
lines are parallel.
● E
●B
● H
● G
INTERIOR
EXTERIOR
EXTERIOR
1 2
3 4
5 6
7 8
WORD BANK:
Alternate Interior Angles
Alternate Exterior Angles Corresponding Angles
Vertical Angles
Consecutive Interior Angles ∡푮푩푪
Consecutive Exterior Angles
∡푫푬푯 ∡ퟒ Transversal
∡ퟓ
∡푨푩푮
∡푯푬푭 Congruent
Supplementary
TRIANGLE’s INTERIOR ANGLE SUM
1. a. First, Create a random triangle on a piece of patty papers.
b. Using your pencil, write a number inside each interior angle a
label.
c. Next, cut out the triangle.
d. Finally, tear off or cut each of the angles from the triangle
e. Using tape, carefully put all 3 angles next to one another so that
they all have the same vertex and the edges are touching but they aren’t overlapping
2. What is the measure of a straight angle or the angle that creates a line by using two opposite rays from a common vertex?
3. Collectively does the sum of your 3 interior angles of a triangle form a straight angle?
What about others in your class?
4. Make a conjecture about the sum of the interior angles of a triangle. Do you think your conjecture will always be true? (please explain using complete sentences)
1
2
3
1
2
3
•
p.18
M. Winking (Section 1-4)
Paste or Tape your 3 vertices here:
• Common Vertex
5. More formally, why do the 3 interior angles of any triangle sum to 180 ̊ ?
Consider ∆ABC. The segment 푨푩 is extended into a line and a parallel line is constructed through the opposite vertex. So, 푨푩⃖ ⃗ ∥ 푪푫⃖ ⃗ . a. Why is ∡ퟏ ≅ ∡ퟐ ?
b. Why is ∡ퟓ ≅ ∡ퟒ ?
c. Why is 풎∡ퟐ + 풎∡ퟑ + 풎∡ퟒ = ퟏퟖퟎ° ?
d. Using substitution we can replace 풎∡ퟐ with 풎∡ퟏ and 풎∡ퟒ with 풎∡ퟓ to show that the
interior angles of a triangle must always sum to 180̊.
() + 풎∡ퟑ + () = ퟏퟖퟎ°
Write the angle number in the and then write the letter that corresponds with the number based on the code at the bottom in the box. 7. Angle 2 and Angle are alternate exterior angles. 8. Angle 7 and Angle are alternate exterior angles. 9. Angle 4 and Angle are corresponding angles. 10. Angle 5 and Angle are consecutive interior angles. 11. Angle 3 and Angle are alternate interior angles. 12. Angle 7 and Angle are consecutive exterior angles. 13. Angle 6 and Angle are vertical angles. 14. Angle 2 and Angle are a linear pair and on the same side of the transversal.
15. Angle 1 and Angle are corresponding angles.
1=D 2=U 3= L 4 = A 5 = N 6 = I 7 = E 8 = C
What type of Geometry is this?
1 2 3 4
5 6 7 8
p.19
M. Winking (Section 1-4)
16. Given lines p and q are parallel, find the value of x that makes each diagram true. a. b.
17. Given lines m and n are parallel, find the value y of that makes each diagram
true. a. b.
18. ANGLE PUZZLE. Find AEF
●
●
●
●
A
B C
D
E
F
● G
40º
m
n
130º
yº
(6x+5)º
(2x+15)º p
q (6x+5)º
(2x+45)º p
q
x = x =
Given: 85m DEF 50m ABG BAE is a right angle CGE and DEG are supplementary
m AEF
40º
m
n 130º yº
y = y =
p.20
M. Winking (Section 1-4)
19. Converse of AIA, AEA, CIA, CEA a.
20. By which property (SSS, AA, SAS)
21. Using (SSS, AA, SAS) which triangles can you determine must be similar? (explain why)
A) B)
D)
10
p
q 70º
120º
Similar? YES NO
SSS AA SAS
circle one
Similar? YES NO
SSS AA SAS
circle one
of AIA, AEA, CIA, CEA. Which sets of lines are parallel and explain
b.
which property (SSS, AA, SAS) are the triangles similar (∆RSQ~∆UST)? Explain why.
Using (SSS, AA, SAS) which triangles can you determine must be similar? (explain why)
C)
E)
50º
Similar? YES NO
SSS AA SAS
circle one
Similar? YES NO
SSS AA SAS
circle one
M. Winking (Section 1-4)
What is the measure of TU?
explain why?
)? Explain why.
Using (SSS, AA, SAS) which triangles can you determine must be similar? (explain why)
p
q 80º
Similar? YES NO
SSS AA SAS
circle one
Similar? YES NO
SSS AA SAS
circle one
p.21
What is the measure of TU?
12
5
6
x
10 cm
6 cm
8 cm x
5 cm
22. Using some type of similar figure find the unknown lengths. A. C.
22a. x =
22c. x =
cm 6 cm
x 3 cm
of similar figure find the unknown lengths.
B. C.
D.
22b. x =
HINT:
M. Winking (Section 1-4)
22c. y =
22d. x =
p.22
Prove the Pythagorean Theorem (a2
+ b2 = c2) using similar right triangles:
M. Winking (Section 1-4)
p.23