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Essential Question. For which of the theorems involving parallel lines and transversals is the converse true? Exploring Converses. Work with a partner. Write the converse of each conditional statement. Draw a diagram to represent the converse. Determine whether the converse is true. Justify your conclusion.
3.3 Proofs with Parallel Lines EXPLORE IT Work with a partner. Write the converse of each conditional statement. Determine whether the converse is true. Justify your conclusion. a. Corresponding Angles Theorem If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 1 4 2 3 6 8 7 5 b. Alternate ...
Math Practice. Analyze Relationships. What is the sum of the measures of a pair of consecutive interior angles? Does it stay the same or change when you adjust the lines? intersects both parallel lines. Find the measures of the eight angles that are formed. What do you notice?
What you should learn. GOAL 1. Prove that two lines are parallel. re parallel. You can use the following postulate and theorems to p. GOAL 2 Use properties of lines are parallel. parallel lines to solve real-life problems, such as proving that prehistoric mounds are parallel in Ex. 19. Why you should learn it. n Exa.
Utilizing Parallel Lines in Proofs Reasons 1) Given 2) Given 3) If parallel lines cut by transversal, then altemate angles are conguent 4) Transitive property 5) If base angles are congruent, then triangle is isosceles AEK BED 1) 2) 5) ABE is isosceles BED EBA BAE BAE or Recognizing the altemate interior angles... Example: Given: Prove: Circle E
1. If two lines are cut by a transversal so that alternate interior angles are (congruent, supplementary, complementary), then the lines are parallel. 2. If two lines are cut by a transversal so that same-side interior angles are (congruent, supplementary, complementary), then the lines are parallel. 3. If two lines are cut by a transversal so ...
Notes: PROOFS OF PARALLEL LINES. Content Objective: I will apply the relationships between the measures of the angle pairs formed by two parallel lines cut by a transversal to proofs. EXAMPLE 1: Use the diagram on the right to complete the following theorems/postulates.
