Module 1- Lesson 7 and 8 Finding Unknown Angle Measures – Transversals and Auxiliary Lines Finding Unknown Angle Measures in Triangles

DO NOW ∡ ∡ ∡ ∡ Module 1 – lesson 7 p. S41 X+8 +2x -8 = 90 3x = 90 Angle Addition Postulate 3x = 90 X = 30 Y = 2x-8 30 𝑜 Verticals Angles Theorem Y = 2(30)-8 52 𝑜 Substitution Y = 60-8 Y = 52 ∡𝐴𝑂𝐶 𝑎𝑛𝑑∡𝐷𝑂𝐵 2x-8 + 4x -24 + BOF = 180 ∡ Adjacent angles on a line Substitution 52 + 4( 30) -24 + BOF = 180 ∡ 52 + (120) - 24 + BOF = 180 ∡ BOF = 32 ∡

a = e, b=f, c=g,d=h c=f , d=e d+f=180 , c+e =180

Corresponding angles are congruent ( = ) 48 𝑜 Corresponding angles are congruent ( = )

Same-side interior angles are supplementary 132 𝑜 Same-side interior angles are supplementary

Alternate Interior angles are congruent ( = ) 48 𝑜 Alternate Interior angles are congruent ( = )

Alternate exterior angles are congruent ( = ) 48 𝑜 Alternate exterior angles are congruent ( = )

Given line m and any point P not on m, there exist exactly one line through P parallel to m If line t is parallel to line d and line d is parallel to line f, then line f is parallel to line t.

Draw line t through point P parallel to lines m and n auxiliary line m t n f = 35 and e = 41 so W = 76 P Draw line t through point P parallel to lines m and n

53 𝑜 53 𝑜 127 𝑜 Vertical angles theorem Same-side interior angles Corresponding angles are congruent ( = ) 53 𝑜 Vertical angles theorem 53 𝑜 127 𝑜 Same-side interior angles are supplementary

145 𝑜 35 𝑜 Corresponding angles are congruent ( = ) Linear pair have a sum of 180

54 𝑜 68 𝑜 Alternate Interior angles are congruent ( = ) 𝟏𝟏𝟐 𝑜 68 𝑜 Corresponding angles are congruent ( = ) Linear pair have a sum of 180

36+56=92 𝑜 36 𝑜 56 𝑜 Alternate Interior angles are congruent ( = ) Same-side Interior angles are supplementary Angle addition postulate

Same-side Interior angles 18 𝑜 82 𝑜 18+82=100 𝑜 Same-side Interior angles are supplementary

114 𝑜

92 𝑜 42 𝑜 46 𝑜

81 𝑜

18 𝑜 94 𝑜

46 𝑜

HOMEWORK

Triangle Angle Sum Theorem 180 𝑜 The sum of the 3 angle measures of any triangle is __________. Triangle Angle Sum Theorem

exterior angle

exterior angle

exterior angle

exterior angle

exterior angle

exterior angle

NOT an exterior angle

NOT an exterior angle

remote interior angles exterior angle non-adjacent or remote interior angles

non-adjacent remote interior In any triangle, the measure of the exterior angle is equal to the sum of the measures of the ___________________angles. These are also known as _______________________________angles. non-adjacent remote interior

Isosceles triangle theorem Base angles of an ____________________ triangle are equal in measure. isosceles Isosceles triangle theorem

Equilateral triangle theorem Each angle of an _________________ triangle has a measure equal to 60°. Equilateral triangle theorem

HOMEWORK