Your Learning Objectives Identify angles formed by parallel

Your Learning Objectives: Identify angles formed by parallel lines and cut by a transversal Apply properties of angles to geometric shapes • Vertical • Corresponding • Alternate • Such as Trapezoids • And Parallelograms

Parallel Lines

Angles formed above and below parallel lines are called Exterior angles and angle formed between parallel lines are called Interior angles Exterior Interior Exterior

Angles Between Parallel lines. Transversal Parallel lines remain the same distance apart. Vertically opposite angles are equal. vert. opp. s Corresponding angles are equal. corr. s

Angles Between Parallel lines Transversal Parallel lines remain the same distance apart. Vertically opposite angles are equal. vert. opp. s Corresponding angles are equal. corr. s Alternate Interior angles are equal. alt. s

Angles Between Parallel lines Transversal Parallel lines remain the same distance apart. Vertically opposite angles are equal. vert. opp. s Corresponding angles are equal. corr. s Alternate angles are equal. alt. s Consecutive Interior angles are Supplementary Int. s AKA “Same Side interior angles”

Angles Between Parallel lines Come in many shapes and sizes

Angles Between Parallel lines Name an angle corresponding to the marked angle. Transversal d h e g a c f Vertically opposite angles are equal. * Alternate angles are equal. Corresponding angles are equal. Interior angles sum to 180 o. (Supplementary) Parallel lines remain the same distance apart. vert. opp. s corr. s alt. s Int. s

Angles Between Parallel lines Name an angle corresponding to the marked angle. Transversal a h e g c b f Vertically opposite angles are equal. * Alternate angles are equal. Corresponding angles are equal. Interior angles sum to 180 o. (Supplementary) Parallel lines remain the same distance apart. vert. opp. s corr. s alt. s Int. s

Angles Between Parallel lines Name an angle corresponding to the marked angle. Transversal d h g a c b f Vertically opposite angles are equal. * Alternate angles are equal. Corresponding angles are equal. Interior angles sum to 180 o. (Supplementary) Parallel lines remain the same distance apart. vert. opp. s corr. s alt. s Int. s

Angles Between Parallel lines Name an angle corresponding to the marked angle. Transversal d e h g a b f Vertically opposite angles are equal. * Alternate angles are equal. Corresponding angles are equal. Interior angles sum to 180 o. (Supplementary) Parallel lines remain the same distance apart. vert. opp. s corr. s alt. s Int. s

Angles Between Parallel lines Name an angle alternate to the marked angle. Transversal d e h g a b f Parallel lines remain the same distance apart. Vertically opposite angles are equal. vert. opp. s Corresponding angles are equal. corr. s Alternate angles are equal. alt. s * Interior angles sum to 180 o. (Supplementary) Int. s

Angles Between Parallel lines Name an angle alternate to the marked angle. Transversal d a b c e h Parallel lines remain the same distance apart. g Vertically opposite angles are equal. vert. opp. s Corresponding angles are equal. corr. s Alternate angles are equal. alt. s * Interior angles sum to 180 o. (Supplementary) Int. s

Angles Between Parallel lines Name an angle interior to the marked angle. Transversal a b c h * d g e Parallel lines remain the same distance apart. Vertically opposite angles are equal. vert. opp. s Corresponding angles are equal. corr. s Alternate angles are equal. alt. s Interior angles sum to 180 o. (Supplementary) Int. s

Angles Between Parallel lines Name an angle interior to the marked angle. Transversal d a b c e h * Parallel lines remain the same distance apart. g Vertically opposite angles are equal. vert. opp. s Corresponding angles are equal. corr. s Alternate angles are equal. alt. s Interior angles sum to 180 o. (Supplementary) Int. s

Angles Between Parallel lines d Name an angle corresponding to the marked angle. * a c h e g f Vertically opposite angles are equal. vert. opp. s Corresponding angles are equal. corr. s Alternate angles are equal. alt. s Interior angles sum to 180 o. (Supplementary) Int. s

Angles Between Parallel lines d Name an angle alternate to the marked angle. * a c b e g f Vertically opposite angles are equal. vert. opp. s Corresponding angles are equal. corr. s Alternate angles are equal. alt. s Interior angles sum to 180 o. (Supplementary) Int. s

Angles Between Parallel lines d Name an angle interior to the marked angle. * c b h e g f Vertically opposite angles are equal. vert. opp. s Corresponding angles are equal. corr. s Alternate angles are equal. alt. s Interior angles sum to 180 o. (Supplementary) Int. s

Angles Between Parallel lines Name in order, the angles that are alternate, interior and corresponding to the marked angle. h g e f d c b Vertically opposite angles are equal. vert. opp. s Corresponding angles are equal. corr. s Alternate angles are equal. alt. s Interior angles sum to 180 o. (Supplementary) Int. s

Angles Between Parallel lines Name in order, the angles that are alternate, interior and corresponding to the marked angle. c g h f d a e Vertically opposite angles are equal. vert. opp. s Corresponding angles are equal. corr. s Alternate angles are equal. alt. s Interior angles sum to 180 o. (Supplementary) Int. s

Angles Between Parallel lines Finding unknown angles z x= 80 o Int. s y= 60 o vert. opp. s z= 120 o Find the unknown angles stating reasons, from the list below. 100 o y Int. s x 60 o Vertically opposite angles are equal. vert. opp. s Corresponding angles are equal. corr. s Alternate angles are equal. alt. s Interior angles sum to 180 o. (Supplementary) Int. s

Angles Between Parallel lines Finding unknown angles 105 o z x x= 105 o y= 55 o alt. s z= 125 o Int. s 55 o corr. s Find the unknown angles stating reasons, from the list below. y Vertically opposite angles are equal. vert. opp. s Corresponding angles are equal. corr. s Alternate angles are equal. alt. s Interior angles sum to 180 o. (Supplementary) Int. s

Angles Between Parallel lines Finding unknown angles Unknown angles in quadrilaterals and other figures can be found using these properties. y x= 85 o Int. s y= 120 o Int. s Find the unknown angles stating reasons, from the list below. 95 o 60 o x Vertically opposite angles are equal. vert. opp. s Corresponding angles are equal. corr. s Alternate angles are equal. alt. s Interior angles sum to 180 o. (Supplementary) Int. s

Angles Between Parallel lines Finding unknown angles Unknown angles in quadrilaterals and other figures can be found using these properties. 125 o Int. s y= 55 o Int. s z= 125 o Int. s 55 o y x o 125 55 o x= 125 zo What does this tell you about parallelograms? Find the unknown angles stating reasons, from the list below. Vertically opposite angles are equal. vert. opp. s Corresponding angles are equal. corr. s Alternate angles are equal. alt. s Interior angles sum to 180 o. (Supplementary) Int. s

Angles Between Parallel lines 58 o e f g h b a 70 o c d Mixing it! a= 58 o vert. opp. s b= 32 o s in tri c= 32 o alt. s d= 58 o s on line e= 58 o corr. s f = 52 o s at a point g= 64 o isos tri h = 64 o isos tri Vertically opposite angles are equal. vert. opp. s Corresponding angles are equal. corr. s Alternate angles are equal. alt. s Interior angles sum to 180 o. (Supplementary) Int. s Angle sum of a triangle (180 o) s in tri Angle on a line sum to (180 o) s on line Base angles isosceles triangle equal. isos tri. Angles at a point sum to 360 o s at point Find the unknown angles stating reasons, from the list below. There may be more than one reason.

Solving Systems of Equations 5 x+y 120 60 * * 2 x+y Vertically opposite angles are equal. vert. opp. s Corresponding angles are equal. corr. s Alternate angles are equal. alt. s Interior angles sum to 180 o. (Supplementary) Int. s