Download Lesson 7A: Solve for Unknown Angles—Transversals

Lesson 8
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
GEOMETRY
Name:___________________________________
Period:________ Date:__________
Lesson 7A: Solve for Unknown Angles—Transversals
Warmup
Directions: Solve any two out of three equations
Check your answer:
1. 4(𝑥 − 2) = 8(𝑥 − 3) − 12
2. 39 − 8𝑛 = −8(3 + 4𝑛) + 3𝑛
3. −7 − 6𝑎 + 5𝑎 = 3𝑎 − 5𝑎
Challenge me 
4. (𝑥 − 1)(𝑥 + 5) = 𝑥 2 + 4𝑥 − 2
Lesson 8
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
GEOMETRY
Name:___________________________________
Period:________ Date:__________
Lesson 8: Solve for Unknown Angles—Transversals
Mini-Lesson
Learning Targets: I can identify all types of angles formed by parallel lines cut by transversal. I can apply the knowledge
of relationships between angles formed by parallel lines cut by a transversal to find the missing angle.
Using the theorems above, what equations can you create from the
diagram at the right?
Congruent: ______ = _____
Type: ________
Supplementary: ____ + ____ = ____
Type: ________
Lesson 8
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
GEOMETRY
Name:___________________________________
Period:________ Date:__________
If we already know two lines are parallel, then we can say…
a. “If two parallel lines are cut by a transversal, then the corresponding angles are
____________________.”
b. “If two parallel lines are cut by a transversal, then the alternate interior angles are
_____________________.”
c. “If two parallel lines are cut by a transversal, then the same side interior angles
are____________________.”
Two lines 𝐴𝐵 and 𝐶𝐷 are parallel if and only if the following types of angle pairs are congruent or
supplementary:
Corresponding Angles are equal in measure.
List all Corresponding angles: ______ ______ ______ ______
Alternate Interior Angles are equal in measure.
List all pairs of Alternate Interior angles: ______ ______
Same Side Interior Angles are supplementary.
List all pairs of Alternate Interior angles: ______ ______
Guided Practice: We do
Example 1) In the diagram below, find the unknown (labeled) angles. Give reasons for your solutions.
𝑚∠𝑎 = _______
Reason:________________________
𝑚∠𝑏 = _______
Reason:________________________
𝑚∠𝑐 = _______
Reason:________________________
Example 2) In the diagram at right, transversal ⃡𝑇𝑈 intersects ⃡𝑃𝑄
and ⃡𝑅𝑆 at V and W, respectively. If 𝑚∠𝑇𝑉𝑄 = 5𝑥 − 22 and
𝑚∠𝑉𝑊𝑆 = 3𝑥 − 10 , which value of x would result in ⃡𝑃𝑄 ∥ ⃡𝑅𝑆 ?
Lesson 8
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
GEOMETRY
Name:___________________________________
Period:________ Date:__________
Lesson 8: Solve for Unknown Angles—Transversals
Classwork
Two lines 𝐴𝐵 and 𝐶𝐷 are parallel if and only if any one of the following conditions are true:

Corresponding Angles are equal in measure.
or

Alternate Interior Angles are equal in measure.
or

Same Side Interior Angles are supplementary:
1. Transversal
intersects
and
, as shown in the diagram below.
Which statement could always be used to prove
a)
b)
c)
and
are supplementary
d)
and
are supplementary
?
2. A transversal intersects two lines. Which condition would always make the two lines parallel?
a) Vertical angles are congruent.
b) Alternate interior angles are congruent.
c) Corresponding angles are supplementary.
d) Same-side interior angles are complementary.
3. Find m ∠ 1 and then m∠ 2. Justify each answer.
m 1  __________because __________________________________
____________________________________________________
m 2  _________because ___________________________________
____________________________________________________
Lesson 8
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
GEOMETRY
Name:___________________________________
4. Find the value of x if
not to scale.
and
Period:________ Date:__________
The diagram is
1
2
3
l
4
5
6
7
5. As shown in the diagram below, lines m and n are cut by transversal p.
If 𝑚∠1 = 4𝑥 + 14 and 𝑚∠2 = 8𝑥 + 10 , lines m and n are parallel when x equals
1) 1
2) 6
3) 13
4) 17
6. In the diagram at right, line p intersects line m and line n.
If 𝑚∠1 = 7𝑥 and 𝑚∠2 = 5𝑥 + 30, lines m and n are parallel
when 𝑥 equals
1) 12.5
2) 15
3) 87.5
4) 105
8
m
Lesson 8
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
GEOMETRY
Name:___________________________________
Period:________ Date:__________
Lesson 8: Solve for Unknown Angles—Transversals
Homework
1. Find the measure of the unknown angle, and give the name of the theorem used.
A.
B.
ma = ________
mb = ________
Theorem:
____________________
Theorem: ________________________
__________________________________
________________________________
C.
D.
mc = ________
md = ________
Theorem:
____________________
Theorem: _______________________
__________________________________
________________________________
2. Line n intersects lines l and m, forming the angles shown in the
diagram at right. Which value of x would prove 𝑙 ∥ 𝑚 ?
1) 2.5
2) 4.5
3) 6.25
4) 8.75
3.
Lesson 8
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
GEOMETRY
Name:___________________________________
Period:________ Date:__________
4. Given that 𝑝 ∥ 𝑞 and 𝑙 ∥ 𝑚 , find the measures of all the numbered angles in the diagram, giving reasons
for each measurement. The first one is done for you.
a.
b.
c.
d.
e.
f.
g.
h.
𝑚∠1 =
𝑚∠2 =
𝑚∠3 =
𝑚∠4 =
𝑚∠5 =
𝑚∠6 =
𝑚∠7 =
𝑚∠8 =
42
_____
_____
_____
_____
_____
_____
_____
by _corresponding angle theorem__ to __Given Angle___.
by ______________________________ to ________________.
by ______________________________ to ________________.
by ______________________________ to ________________.
by ______________________________ to ________________.
by ______________________________ to ________________.
by ______________________________ to ________________.
by ______________________________ to ________________.
5. Lines p and q are intersected by line r, as shown at right. If 𝑚∠1 = 7𝑥 − 36
and 𝑚∠2 = 5𝑥 + 12 , for which value of x would 𝑝 ∥ 𝑞 ?
6. Peach Street and Cherry Street are parallel. Apple Street intersects them, as
shown in the diagram at right. If 𝑚∠1 = 2𝑥 + 36 and 𝑚∠2 = 7𝑥 − 9 ,
what is 𝑚∠1 ?
7. Find the measures of all the angles given that 𝑙 ∥ 𝑚 .
𝑚∠𝑎 = _______ Reason:______________________
𝑚∠𝑏 = _______ Reason:______________________
𝑚∠𝑐 = _______ Reason:______________________