Download Lesson 3: Solve for Unknown Angles—Transversals

Lesson 3
RCSD Geometry Local MATHEMATICS CURRICULUM
Name:___________________________________ Period:________ Date:__________
U7
GEOMETRY
Lesson 3: Solve for Unknown Angles—Transversals
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.
New Vocabulary: A transversal is a line that intersects two or more lines (in the same plane).
Remember that:
- the word INTERIOR means BETWEEN the lines.
- the word EXTERIOR means OUTSIDE the lines.
- the word ALTERNATE means "alternating sides" of the transversal
When the lines are NOT parallel
When the lines are parallel...
"Names" given to pairs of angles formed by two parallel lines cut by a transversal
• alternate interior angles
• corresponding angles
• alternate exterior angles
• same-side interior angles
Alternate interior angles are "interior" (between the parallel lines),
and they "alternate" sides of the transversal
Identify the pairs of alternate interior angle
__________________________
If two parallel lines are cut by a transversal, the alternate interior angles are
congruent.
Converse
If two lines are cut by a transversal and the alternate interior angles are
congruent, the lines are parallel.
RCSD Geometry Local MATHEMATICS CURRICULUM
Lesson 3
Name:___________________________________ Period:________ Date:__________
U7
GEOMETRY
Alternate exterior angles are "exterior" (outside the parallel lines), and they
"alternate" sides of the transversal
Identify all the pairs of alternate exterior angles ___________
_______________
If two parallel lines are cut by a transversal, the alternate exterior angles
are congruent.
Converse
If two lines are cut by a transversal and the alternate exterior angles are
congruent, the lines are parallel.
If you copy one of the corresponding angles and you translate it along the
transversal, it will coincide with the other corresponding angle.
Identify all the pairs of coresponding angles __________________________
If two parallel lines are cut by a transversal, corresponding angles are
congruent.
Converse
If two lines are cut by a transversal and corresponding angles are
congruent, the lines are parallel.
The "interior" angles same side (between the parallel lines), are on the
same side of the transversal.
Identify all the pairs __________________________
If two parallel lines are cut by a transversal, same-side interior angles are
supplementary
Converse
If two lines are cut by a transversal and the same-side interior angles are
supplementary, the lines are parallel
Lesson 3
RCSD Geometry Local MATHEMATICS CURRICULUM
Name:___________________________________ Period:________ Date:__________
U7
GEOMETRY
Using the theorems above, what equations can you create from the diagram at the right?
Congruent: ______ = _____
Type: ________
Supplementary: ____ + ____ = ____ Type: ________
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: ______ ______
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
Given the diagram at the right with straight lines m, n and t.
Which statement could always be used to prove 𝑚 || 𝑛 ?
Choose:
∠2 and ∠6 are supplementary
m∠2 = m∠3
∠3 and ∠5 are supplementary
m∠5 = m∠7
1.
Lesson 3
RCSD Geometry Local MATHEMATICS CURRICULUM
Name:___________________________________ Period:________ Date:__________
U7
GEOMETRY
Lesson 3: 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 ___________________________________
____________________________________________________
RCSD Geometry Local MATHEMATICS CURRICULUM
Lesson 3
Name:___________________________________ Period:________ Date:__________
In 4 and 5 , use the diagram at the right.
4. Given ∠2 ≅ ∠6, what justifies k || m.
a. Converse Alternate Interior Angles Theorem
b. Converse Alternate Exterior Angles Theorem
c. Converse Corresponding Angles Theorem
d. there is not enough info to state parallel
5. Given n || p , what justifies ∠1 ≅ ∠12
a. Alternate Interior Angles Theorem
b. Alternate Exterior Angles Theorem
c. Corresponding Angles Theorem
d. there is not enough info to make this statement
In 6 and 7, use the diagram at the right.
6. Determine the relationship between ∠1 & ∠10.
a. Alternate Interior
b. Same-side Interior
c. Corresponding Angles
d. None of these
7. Determine the relationship between ∠5 & ∠15.
a. Alternate Exterior
b. Alternate Interior
c. Same-side Interior
d. None of these
8. If m∠9 = 62°, then find the measure the following angles:
a. m∠1=
b. m∠2=
c. m∠4=
d. m∠5=
e. m∠15=
U7
GEOMETRY
RCSD Geometry Local MATHEMATICS CURRICULUM
Lesson 3
Name:___________________________________ Period:________ Date:__________
9.
Given straight lines p, q, t, and s and angles as
marked.
Which value of x will make lines p and q parallel?
Choose:
73º
87º
107º
113º
Given the diagram shown at the right. Assume all lines
are straight.
Find the measures of all of the numbered angles 1
through 12.
m∠1 ________________
m∠2 ________________
m∠3 _________________
m∠4 _________________
m∠5 ________________
m∠6 _________________
m∠7 _________________
m∠8 _________________
m∠9 _________________
m∠10 _________________
m∠11 _________________
m∠12 _________________
U7
GEOMETRY
Lesson 3
RCSD Geometry Local MATHEMATICS CURRICULUM
Name:___________________________________ Period:________ Date:__________
U7
GEOMETRY
Lesson 3: 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: _______________________
____________________
__________________________________
________________________________
RCSD Geometry Local MATHEMATICS CURRICULUM
Lesson 3
Name:___________________________________ Period:________ Date:__________
U7
GEOMETRY
2. 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. 𝑚∠1 = 42
by _corresponding angle theorem__ to __Given Angle___.
b. 𝑚∠2 = _____ by ______________________________ to ________________.
c. 𝑚∠3 = _____ by ______________________________ to ________________.
d. 𝑚∠4 = _____ by ______________________________ to ________________.
e. 𝑚∠5 = _____ by ______________________________ to ________________.
f. 𝑚∠6 = _____ by ______________________________ to ________________.
g. 𝑚∠7 = _____ by ______________________________ to ________________.
h. 𝑚∠8 = _____ by ______________________________ to ________________.
3. Find the measures of all the angles given that 𝑙 ∥ 𝑚 .
𝑚∠𝑎 = _______ Reason:______________________
𝑚∠𝑏 = _______ Reason:______________________
𝑚∠𝑐 = _______ Reason:______________________