1 Learning Target : I can identify and calculate the measure of corresponding angles. Today's lesson will be on a new type of angle called corresponding angles. These type of angles are formed when two parallel line are cut by a line segment called a transversal. We know that parallel lines are two lines that run in the same direction, and NEVER intersect, but the transversal is a line segment that cuts through the two lines and forms multiple types of angles.
Transcript
1
Learning Target: I can identify and calculate the measure of corresponding angles.
Today's lesson will be on a new type of angle called corresponding angles. These type of angles are formed when two parallel line are cut by a line segment called a transversal.
We know that parallel lines are two lines that run in the same direction, and NEVER intersect, but the transversal is a line segment that cuts through the two lines and forms multiple types of angles.
2
Parallel Lines cut by a Transversal
Transversal
A line segment that intersects two parallel lines creating adjacent supplementary angles that correspond to one
another
3
Using the diagram below, describe the relationship between:
a.) ∠1 and ∠2
b.) ∠3 and ∠4
c.) ∠2 and ∠4
d.) ∠1 and ∠3
e.) ∠5 and ∠6
f.) ∠7 and ∠8
g.) ∠5 and ∠7
h.) ∠6 and ∠8
supplementary
supplementary
vertical
vertical
supplementary
supplementary
vertical
vertical
4
Looking at the diagram, can you make a connection between:
a.) ∠1 and ∠5?
b.) ∠2 and ∠6?
They look like they are the same but on is at the top and the other is at the bottom.
5
Pretend we were able to pick up this line and place it on top of the line on the bottom. How can you compare the angles on the given line to the line at the bottom?
113o
113o67o
67o
113o
113o67o
67o
Corresponding Angles
Angles that are in the same placement on the same side of the transversal. These angles will
always be congruent. **Think about picking one line up and placing it on top of another
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Understanding Corresponding Angles
Given that m∠5 = 124o, what is the measure of ∠1? And why can we identify it?
124o
234
678
1 ∠1 = 124° ∠5 = 124°
7
Understanding Corresponding Angles
Given that m∠2 = 78o, what is the measure of ∠6? And why can we identify it?
78o
5
34
678
1 ∠2 =78° ∠6 = 78°
8
Given that m∠5 = 124o, find the measures of the 7 remaining angles.
124o
234
678
1
∠1 = 124° ∠5 = 124°
∠2 = 56° ∠6 = 56°
∠3 = 124° ∠7 = 124°
∠4 = 56° ∠8 = 56°
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If the m∠1 = 45°, what is the measure of angle 5?
m∠5 is also 45° because it is corresponding to angle 1.
10
Which angle corresponds to ∠3? If the m∠3 is 126°, what is the measure of angle 7?
∠7 corresponds to ∠3 because it is on the same side of the transversal, in the same position. It is also 126°.
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Now what happens when we have to solve? So knowing that corresponding angles are congruent, we can set our two angles equal to each other to solve:
x + 64 = 138° 64 64x = 74
To check, we replace x with 74 and see if the total is 138:
74 + 64 = 138
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Solve for x, then find the measure of each angle.We can tell that these are corresponding angles because they are in the same place on the same side of the transversal, and since corresponding angles are congruent, we can set these expressions equal to one another to solve.
x + 64 = 3x 26x x
64 = 2x 26+ 26+ 26
90 = 2x22
45 = x
45 + 64 = 109°
3(45) 26 = 109°
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PROBLEM SET: Today you will be given 5 problems to complete. Please make sure to show all work in order to receive full credit!
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1.) Given that m∠2 = 78o, find the measures of the 7 remaining angles.
78o34
678
1∠1 = ∠5 =
∠2 =78° ∠6 =
∠3 = ∠7 =
∠4 = ∠8 =5
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If angle d = 60 degrees, what is the measure of angle h? ____
What kind of angles are b and t?
What kind of angles are d and h?
2.)
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Problem Set #s 3 & 4 Solve for x, then check to see if your angle is congruent.
102o
(x + 27)o
(3x 1)o
o56
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Problem Set #5 Solve for x, then find the measures of ∠s 4 & 8.
