Download 5-2 Parallel Line Theorems Day 2

Geometry/Trig
Name: ______________________
Lesson 5-2: Parallel Line Theorems
Learning Goals: (#2) What are the parallel line theorems? How can we solve application questions
using parallel line theorems?
In the last lesson, we learned about 5 angle relationships that are created when two parallel lines are cut by
a transversal. We refer to these five relationships as the parallel line theorems. Let’s recap them and revisit
multi-step applications!
Warm-Up
1. List a pairs of angles for each of the following types of angle pairs
and their relationship when lines parallel:

Alternate interior angles, such as __∠3 and__ _____, are ________________ when lines are parallel.
If these angles were not _________, then _______________________________________________________________________________.

Same side interior angles, such as ______________, are _________________when lines are parallel.
If these angles were not _________, then _______________________________________________________________________________.

Alternate exterior angles, such as ______________, are _________________when lines are parallel.
If these angles were not _________, then the lines would not be parallel.

Same side exterior angles, such as ______________, are _________________when lines are parallel.
If these angles were not _________, then then the lines would not be parallel.

Corresponding angles, such as ______________, are _________________when lines are parallel.
Geometry/Trig
If these angles were not _________, then then the lines would not be parallel.
2. Calculate the measure of the indicated angles.
Type: _______________________________
Relationship (if lines parallel): ____________________________
Missing Angle:
Type: _______________________________
Relationship (if lines parallel): ____________________________
Missing Angle:
Watch Me!
⃡ ∥ 𝐶𝐷
⃡ , and transversal 𝐸𝐹
⃡ and 𝐶𝐷
⃡ at G and H, respectively. If
⃡ intersects 𝐴𝐵
3. In the accompanying diagram, 𝐴𝐵
𝑚∠𝐷𝐻𝐺: 𝑚∠𝐵𝐺𝐻 𝑎𝑟𝑒 𝑖𝑛 𝑎 𝑟𝑎𝑡𝑖𝑜 𝑜𝑓 1: 2, find 𝑚∠𝐷𝐻𝐺.
*Note!
When we read “in a ratio of…”
1. Identify the angle pair name
and relationship.
2. Place each number next to a
variable and solve normally.
Geometry/Trig
4. In the diagram below,
and
at R. If
, find
.
*Key Notes as we solve…
You Try!
5. In the accompanying diagram, ⃡𝐴𝐶 ∥ ⃡𝐸𝐺 , and transversal ⃡𝐷𝐻 intersects ⃡𝐴𝐶 and ⃡𝐸𝐺 at B and F, respectively. If
𝑚∠𝐷𝐵𝐶: 𝑚∠𝐻𝐹𝐺 𝑎𝑟𝑒 𝑖𝑛 𝑎 𝑟𝑎𝑡𝑖𝑜 𝑜𝑓 3: 2, find 𝑚∠𝐻𝐹𝐺.
Geometry/Trig
6. In the diagram below, find the measure of all of the interior angles of triangle MTR.
*Look at #4 in notes,
if you are stuck!!
7.
*Hint: If Elm and Oak are parallel, what
relationship do the two indicated angles have?
8. Solve for x and the measure of each indicated angle. Be sure to show your work!
*Hint: Are these two
angles a special angle
pair?
If not, can you fill in more
of the diagram with the
Geometry/Trig
9. State the type of angles and their relationship based on the diagram below, then solve for the measure of the
angles.
Type: _______________________________
Relationship (if lines parallel): ____________________________
Missing Angle:
10. Solve for x.
12. Find the measure of the angle indicated in bold.
11. Solve for x:
13. Find the measure of the angle indicated in bold.
Geometry/Trig