1.Using the figure on the right, classify the relationship between ...
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1. Using the figure on the right, classify the relationship between <1 and <4
2. Using the figure on the right, find the measure of each angle.
m<9 = 2x – 4
m<10 = 2x +4
PROBLEMS OF THE DAY/HOMEWORK QUIZ!
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You named angle pairs formed by parallel lines and transversals.
• Use theorems to determine the relationships between specific pairs of angles.
• Use algebra to find angle measurements.
3.2 Angles and Parallel Lines
Use Theorems about Parallel Lines
FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m2 = 125, find m3.
2 3 Alternate Interior Angles Theorem
m2 = m3 Definition of congruent angles
125 = m3 Substitution
Answer: m3 = 125
A. ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x.
Find Values of Variables
5 7 Corresponding Angles Postulate
m5 = m7 Definition of congruent angles
2x – 10 = x + 15 Substitution
x – 10 = 15 Subtract x from each side.
x = 25 Add 10 to each side.
Answer: x = 25
B. ALGEBRA If m4 = 4(y – 25), and m8 = 4y, find y.
Find Values of Variables
8 6 Corresponding AnglesPostulate
m8 = m6 Definition of congruentangles
4y = m6 Substitution
Find Values of Variables
m6 + m4 = 180 Supplement Theorem
4y + 4(y – 25) = 180 Substitution
4y + 4y – 100 = 180 Distributive Property
8y = 280 Add 100 to each side.
y = 35 Divide each side by 8.
Answer: y = 35
• In summary,
When you have parallel lines and a transversal, you will have
-Congruent corresponding angles
-Congruent alternate interior angles
-Congruent alternate exterior angles
-Supplementary consecutive angles
-Congruent vertical angles **These are always congruent
You can use these “facts” to solve for unknown angles and values of x!