3 1 Lines and Angles Objective To Identify

3. 1 Lines and Angles

Objective: • To Identify relationships between figures in a square • To identify angles formed by two lines and a transversal. 3. 1 Lines and Angles

Vocabulary: 3. 1 Lines and Angles

Vocabulary • Transversal – a line that intersects two coplanar lines at two distinct points. 3. 1 Lines and Angles

Vocabulary • Interior angles – Angles that are in between the two lines cut by a transversal <3, <4, <5, <6 3. 1 Lines and Angles

Vocabulary • Exterior angles – Angles that are outside the two lines cut by a transversal <1, <2, <7, <8 3. 1 Lines and Angles

Vocabulary • Alternate interior angles < 3 and < 6 < 4 and < 5 3. 1 Lines and Angles

Vocabulary • Alternate exterior angles < 2 and < 7 < 1 and < 8 3. 1 Lines and Angles

Vocabulary • Corresponding Angles – angles that can “overlap” < 1 and < 5 < 2 and < 6 < 3 and < 7 < 4 and < 8 3. 1 Lines and Angles

Vocabulary • Same Side Interior Angles < 4 and < 5 < 3 and < 6 3. 1 Lines and Angles

Vocabulary • Same Side Exterior Angles < 1 and < 8 < 2 and < 7 3. 1 Lines and Angles

Corresponding Angles Postulate • If a transversal intersects two parallel lines, then corresponding angles are congruent m< 1 = m< 2 3. 1 Lines and Angles

Alternate Interior Angles Theorem • If a transversal intersects two parallel lines, then alternate interior angles are congruent m< 5 = m< 6 m< 7 = m< 8 3. 1 Lines and Angles

Same-Side Interior Angles Theorem • If a transversal intersects two parallel lines, then same side interior angles are supplementary 0 120 + 0 60 = 0 180 3. 1 Lines and Angles

Alternate Exterior Angles Theorem • If a transversal intersects two parallel lines, then alternate exterior angles are congruent m< 1 = m< 2 m< 3 = m< 4 3. 1 Lines and Angles

Same-side Exterior Angles Theorem • If a transversal intersects two parallel lines, then same side exterior angles are supplementary 3. 1 Lines and Angles

Angle Relations: 3. 1 Lines and Angles

Angle Relations: 3. 1 Lines and Angles

Examples – interwrite activity • Random problems with different theorems 3. 1 Lines and Angles

Parallelogram Problem 3. 1 Lines and Angles

Parallelogram Problem 7 x – 5 + (115) = 180 7 x + 110 = 180 7 x = 70 x = 10 5 y + 115 = 180 5 y = 65 y = 13 3. 1 Lines and Angles

Lesson Check 3. 1 Lines and Angles

Lesson Check 3. 1 Lines and Angles