Download Math 350 Section 1.2 Answers to Classwork CW1: The segment is

Math 350
Section 1.2
Answers to Classwork
CW1: The segment is perpendicular to the base because we are folding one of the two angles
formed by the segment and the base onto the other angle formed by them, showing that the two
angles are congruent. By Homework 4 in Section 1.1, this means the angles are right angles.
CW2: We have folded the three angles of the triangle so they are side by side, and their exterior
sides form a straight angle. This means the sum of the measures of the angles must be 180
degrees.
CW3: (a) Since the base is parallel to the line through the other vertex A, by Theorem 1.1 the
alternate interior angles formed when the other sides of the triangle cross these lines must be
congruent. This means angles 1 and 4 are congruent, as are angles 3 and 5.
(b) As in CW2, these three angles are side by side, and their exterior sides form a straight angle.
(c) By (b) we know that the measures of angles 2, 4, and 5 add up to 180 degrees. By (a) we may
substitute angle 1 for angle 4, and angle 3 for angle 5, in that statement. So the sum of the
measures of angles 1, 2, and 3 is 180 degrees.
CW4: (a) A hexagon could be divided into 4 triangles by drawing the diagonals from a fixed
vertex, so the sum of the angle measures in a hexagon is 4 x 180* = 720 ° .
(b) From the patterns in the data so far we infer: In general, a polygon with n sides could be
divided into n - 2 triangles by drawing the diagonals from a single vertex.
CW5: The sum of the interior angles in a 10-sided polygon is (10 – 2) x 180 = 1440 ° .
CW6: Is a rhombus always regular? No. Why? The angles need not all be congruent. What do
we call a regular quadrilateral? A square.
CW7: By Theorem 1.6 the sum of the measures of the interior angles of a polygon with n sides
is (n – 2) x 180 degrees. In a regular polygon all these angles are congruent, so the measure of
each is found by dividing (n – 2) x 180 by n.
CW 8: (a) (8 – 2) x 180 = 1080 degrees
(c) 360 / 8 = 45 degrees
(b) 1080 / 8 = 135 degrees
CW 9: Solve
n−2
× 180° = 165° 180n − 360 = 165n 15n = 360 n = 24
n
CW10: Solve
360
= 20 360 = 20n n = 18
n