Download Midterm Review #5

Geometry/Trig
VIDEO
LESSON
Name: ______________________________
Date: _______________________________
Midterm Review 5 - Parallel Line Theorems (Unit 5)
The Learning goals we achieved in these units were…
1. How do we determine if two lines are parallel?
2. What kind of special angles are formed given two parallel
lines and a transversal?
3. How can I the relationship between special angles given two
lines are parallel?
4. How can I determine if two lines are parallel given two lines
and a transversal, and justify my answer?
Special Angle Types
Vertical angles
Supplementary angles
Alternate Interior
Angles
Alternate Exterior
Angles
Example
Description
Across from each other over a vertex
Relationships
Always _______________
Adjacent angles that form a line
two angles that add
up to ________ degrees
Opposite sides of the transversal and
inside the lines
Opposite sides of the transversal and
outside the lines
Corresponding angles
In the “same position” or “same corner”
of the transversal & lines
Same-side interior
Same side of the transversal and inside
the lines
Same side exterior
angles
Justifying that Lines
are Parallel
Same side of the transversal and outside
the lines
________________________
when lines are∥
________________________
when lines are∥
________________________
when lines are∥
________________________
when lines are∥
________________________
when lines are∥
When justifying parallel lines you need to include
1. Type of angle pair
2. Relationship
3. State if the relationship is true (from diagram)
4. Conclusion
1. In the diagram below, m∠AEC = 3x + 30 and m∠CED = 2x - 5. Find the m∠AEC.
Geometry/Trig
2. Using the picture at the right, state the type and relationship for each pair of angles given. Solve if asked.
(a) ∠1 𝑎𝑛𝑑 ∠5
Type: __________________________________________________
Relationship if lines ||: ________________________________________
(b) ∠4 𝑎𝑛𝑑 ∠5
Type: __________________________________________________
Relationship if lines ||: ________________________________________
(c) What type of special angle pair are ∠4 and ∠6? __________________________________________________
You are given that m∠4 = 81o. What is the m∠6?
(d) You are given that ∠1 = 7x+20 and ∠8 = 9x – 2. What is the m∠8?
3. Investigate the diagram below. Is AB is parallel to CD in the following diagram? EXPLAIN YOUR REASONING
Geometry/Trig
« «
«
4. In the accompanying diagram, AB , CD and EF intersect at G. If ∠𝐷𝐺𝐵 = 20 𝑑𝑒𝑔𝑟𝑒𝑒𝑠 and∠𝐹𝐺𝐶 = 72 𝑑𝑒𝑔𝑟𝑒𝑒𝑠,
find the measurement of ∠1, ∠2. ∠3, 𝑎𝑛𝑑 ∠4
 ∠1 = ______________

∠2 = ______________

∠3 = ______________

∠4 = ______________
5. In the accompanying diagram, ⃡𝐴𝐵 ∥ ⃡𝐶𝐷, and transversal ⃡𝐸𝐹 intersects ⃡𝐴𝐶 and ⃡𝐸𝐺 at G and H, respectively. If
𝑚∠𝐵𝐺𝐻: 𝑚∠𝐷𝐻𝐺 𝑎𝑟𝑒 𝑖𝑛 𝑎 𝑟𝑎𝑡𝑖𝑜 𝑜𝑓 3: 6, find 𝑚∠𝐵𝐺𝐻.
6. Solve for angles 1, 2, and 3 in the diagram below.
Show your work clearly!
m∠1 = ______________________
m∠2 = ______________________
m∠3 = ______________________