Warm Up Identify each of the following terms or objects. 1. points that lie in the same plane
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Transcript of Warm Up Identify each of the following terms or objects. 1. points that lie in the same plane
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Warm Up
Identify each of the following terms or objects.1. points that lie in the same plane
2. two angles whose sum is 180°
3. the intersection of two distinct intersecting lines
4. a pair of adjacent angles whose non-common sides are opposite rays
2.6 Lines and Angles
Coplanar points
Supplementary angles
A point
Linear pair of angles
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ObjectivesProve and use theorems about the angles formed by parallel lines and a transversal.
2.6 Lines and Angles
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Example 1:
Give an example of each angle pair.
A. corresponding angles
B. alternate interior angles
C. alternate exterior angles
D. same-side interior angles
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Postulate or Theorem Hypothesis ConclusionCorresponding Angles Postulate
Alternate interior Angles Theorem
Alternate Exterior Angles Theorem
Same-Side Interior Angles Theorem
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When two parallel lines are cut by a transversal, any pair of angles will either be __________________ or _____________________.congruent supplementary
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Example 2:
Find mQRS.
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Example 3:
Find each angle measure.
A. mDCE
B. mECF
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Example 4:
Find mABD.
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Example 5:
Find mABD.
Finished 1st amd 3rd hour
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35°
Example 6:Find the measure of all numbered angles in the diagram.
1 =2 =3 =4 =5 =
6 =7 =8 =9 =10 =
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Example 7:Proof of the Alternate Exterior Angles TheoremGiven: Prove:
Statements Reasons1. 1.2. 2.3. 3.4. 4.
𝑙 ∥𝑚∠1≅∠2∠2≅∠3∠1≅∠3
GivenCorresp. PostVert. Thm.Trans. Prop
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Example 8:
𝑚∠2+𝑚∠3=180 °Corresp. Post.
𝑚∠1=𝑚∠2𝑚∠1+𝑚∠3=180 ° Subst. Prop.