Congruent Angles Associated with Parallel Lines. Parallel Postulate: Through a point not on a line, there is exactly one parallel to the given line. a.

Slides:



Advertisements
Similar presentations
Angles and Parallel Lines
Advertisements

Angles and Parallel Lines
PARALLEL LINES AND TRANSVERSALS. CORRESPONDING ANGLES POSTULATE Two lines cut by a transversal are parallel if and only if the pairs of corresponding.
Properties of Lines and Transversals
Geometry vocabulary Mr. Dorn. Corresponding Angles Postulate If two parallel lines are cut by a transversal, then each pair of corresponding angles is.
1Geometry Lesson: Aim: How do we prove lines are parallel? Do Now: 1) Name 4 pairs of corresponding angles. 2) Name 2 pairs of alternate interior angles.
Use Parallel Lines and Transversals
PARALLEL LINES and TRANSVERSALS.
Lesson 3-4 Proving lines parallel,. Postulates and Theorems Postulate 3-4 – If two lines in a plane are cut by a transversal so that corresponding angles.
3.2 Properties of Parallel Lines Objectives: TSW … Use the properties of parallel lines cut by a transversal to determine angles measures. Use algebra.
5.3 Congruent Angles Associated With Parallel Lines Objective: After studying this section, you will be able to: a. apply the parallel postulate, b. identify.
1 Angles and Parallel Lines. 2 Transversal Definition: A line that intersects two or more lines in a plane at different points is called a transversal.
3.3 Parallel Lines & Transversals
Angles and Parallel Lines
Proving lines parallel Chapter 3 Section 5. converse corresponding angles postulate If two lines are cut by a transversal so that corresponding angles.
PROVING LINES PARALLEL. CONVERSE OF  … Corresponding Angles Postulate: If the pairs of corresponding angles are congruent, then the lines are parallel.
Properties of Parallel Lines Geometry Unit 3, Lesson 1 Mrs. King.
Lesson 2-5: Proving Lines Parallel 1 Lesson Proving Lines Parallel.
3.2 Proving Lines Parallel
Geometry Section 3.2 Use Parallel Lines and Transversals.
Warm Up Week 1 1) If ∠ 1 and ∠ 2 are vertical angles, then ∠ 1 ≅ ∠ 2. State the postulate or theorem: 2) If ∠ 1 ≅ ∠ 2 and ∠ 2 ≅ ∠ 3, then ∠ 1.
PARALLEL LINES AND TRANSVERSALS SECTIONS
Section 3.5 Properties of Parallel Lines. Transversal  Is a line that intersects two or more coplanar lines at different points.  Angles formed:  Corresponding.
LINES CUT BY A TRANSVERSAL. 3Geometry Lesson: Proving Lines are Parallel.
Angle Relationships. Vocabulary Transversal: a line that intersects two or more lines at different points. Transversal: a line that intersects two or.
Congruent Angles Associated with Parallel Lines.  Most Theorems in this section are converses of what we learned in sec 5-2  In this section we start.
Section 3-3 Parallel Lines and Transversals. Properties of Parallel Lines.
Parallel Lines and Angles Objectives Define transversal and the angles associated with a transversal State and apply the properties of angles.
Warm-Up Classify the angle pair as corresponding, alternate interior, alternate exterior, consecutive interior or.
Triangles and Lines – Angles and Lines When two lines intersect they create angles. Some special relationships occur when the lines have properties such.
3.2: Properties of Parallel Lines 1. Today’s Objectives  Understand theorems about parallel lines  Use properties of parallel lines to find angle measurements.
Section 3.2 Parallel Lines and Transversals Learning Goal: Students will identify congruent angles associated with parallel lines and transversals and.
 Transversal: a line that intersects two coplanar lines at two different points. T (transversal) n m
3-2 Properties of Parallel Lines. 2) Postulate 10: Corresponding Angles Postulate If two parallel lines are cut by a transversal then the pairs of corresponding.
Corresponding Angles Postulate If a transversal intersects 2 || lines, then corresponding s are .
3.4 Parallel Lines and Transversals
3.2- Angles formed by parallel lines and transversals
PROPERTIES OF PARALLEL LINES POSTULATE
Proving Lines are Parallel
3-2 Properties of Parallel Lines
3.3 Parallel Lines and Transversals
3.4 Proving that Lines are Parallel
3-1 Properties of Parallel Lines
Proving Lines are Parallel
Warm Up Word Bank Vertical Angles Congruent Angles Linear Pair Parallel Lines Skew Lines – Lines that do not intersect and are not coplanar.
Properties of Parallel Lines
Use Parallel Lines and Transversals
Proving Lines Parallel
Parallel Lines and Angles
Chapter 3.2 Notes: Use Parallel Lines and Transversals
Parallel Lines and Transversals
3.5 Properties of Parallel Lines
Transversals and Parallel Lines
3.2- Angles formed by parallel lines and transversals
Lesson 3.2 Use Parallel Lines and Transversals
3.2 Use || Lines and Transversals
Use Parallel Lines and Transversals
3-2 Properties of Parallel Lines
Parallel Lines and Transversals
Angles and Parallel Lines
Proving Lines Parallel
Module 14: Lesson 3 Proving Lines are Parallel
Angles and Parallel Lines
Properties of parallel Lines
Parallel Lines and Transversals
Parallel Lines and Transversals
3.2 Parallel Lines and Transversals …..
3.2 Notes: Use Parallel Lines and Transversals
Angles and Parallel Lines
Presentation transcript:

Congruent Angles Associated with Parallel Lines

Parallel Postulate: Through a point not on a line, there is exactly one parallel to the given line. a P

Notice the special tick marks ( ) used to designate parallel lines.

Six Theorems About Parallel Lines

If two parallel lines are cut by a transversal, then Each pair of alternate interior angles are congruent Each pair of alternate exterior angles are congruent Each pair of corresponding angles are congruent Each pair of interior angles on the same side of the transversal are supplementary Each pair of exterior angles on the same side of the transversal are supplementary.

Since alt. int.  s are , 3x + 5 = 2x + 10 x + 5 = 10 x = 5 3(5) + 5 = 20 Because vertical  s are , m  1 = 20.

1.FA ║ DE 2.  A   D 3.FA  DE 4.AB  CD 5.AC  BD 6.ΔFAC  ΔEDB 7.  F   E 1.Given 2.║ lines → alt. int.  s  3.Given 4.Given 5.Addition Property (BC to step 4) 6.SAS (3, 2, 5) 7.CPCTC

Using the Parallel Postulate, draw m parallel to a.  2 &  3 are congruent (alt. int.  s are  )  3 = 40°  4 &  5 are supplementary.  4 = 80°  1 = 40° + 80° = 120° m

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2025 SlidePlayer.com. Inc. All rights reserved.