FINAL EXAM REVIEW Chapter 3 Key Concepts

Chapter 3 Vocabulary parallelskewtransversal corresponding <‘s alternate interior <‘s same-side interior <‘s triangle scalene Δ isosceles Δ equilateral Δ exterior < interior < remote interior < polygonvertexdiagonal inductive reasoning

Theorem If two parallel planes are cut by a third plane, then the lines of intersection are parallel. j k j // k

Postulate If two // lines are cut by a transversal, then corresponding angles are congruent. If two // lines are cut by a transversal, then corresponding angles are congruent. // Lines => corr. <‘s = ~ Example: <1 = <5 ~ corr. // Lines ~ CONVERSE

Theorem If two // lines are cut by a transversal, then alternate interior angles are congruent. If two // lines are cut by a transversal, then alternate interior angles are congruent. // Lines => alt int <‘s = ~ Example: <3 = <6 ~ CONVERSEalt int // Lines ~

Theorem If two // lines are cut by a transversal, then same side interior angles are supplementary. If two // lines are cut by a transversal, then same side interior angles are supplementary. // Lines => SS Int <‘s supp Example: <4 is supp to <6 CONVERSESS Int // Lines

Theorem If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line. If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line. In a plane two lines perpendicular to the same line are parallel. CONVERSE

3 More Quick Theorems Theorem:Through a point outside a line, there is exactly one line parallel to the given line. Theorem:Through a point outside a line, there is exactly one line perpendicular to the given line. Theorem:Two lines parallel to a third line are parallel to each other...

1.Show that a pair of Corr. <‘s are = 2. Alt. Int. <‘s are = 3. S-S Int. <‘s are supp 4.Show that 2 lines are to a 3 rd line 5. to a 3 rd line 5 Ways to Prove 2 Lines Parallel ~ ~

Theorem TThe sum of the measures of the angles of a triangle is 180. A C B m<1 + m<2 + M<3 = 180

Corollaries (Off-Shoots) of the Previous Theorem abab 1) If two angles of a triangle are congruent to two angles of another triangle, then the third angles are congruent. cc 2) Each angle of an equilateral triangle has measure ) In a triangle, there can be at most one right angle or obtuse angle. 4) The acute angles of a right triangle are complementary. a bc <a and <b are complementary

Theorem  The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interiors. a b c m<a = m<b + m<c Example: = 150

Theorem The sum of the measures of the interior angles of a convex polygon with n sides is (n-2)180. Example: 5 sides. 3 triangles. Sum of angle measures is (5-2)(180) = 3(180) = 540

Theorem The sum of the measures of the exterior angles of any convex polygon, one angle at each vertex, is 360.

Homework ► pg. 111 Chapter Review (skip 16) ► pg. 112 Chapter Test (skip 13)