University:
California State University, Northridge
Course:
MATH 370 | Foundations of Geometry
Academic year:

2024
Views:

387

Pages:

5
Author:

Makhi Crane

Homework for Section 3.1 Problem 1 Exercise 1.1: Students use a protractor to measure angles to justify these facts. Exercise 1.2: a) The activity used to justify the fact that the sum of the measures of the three angles of a triangle is 180° is the same activity described on page 37 of our textbook. Students copy a triangle, cut off the corners, and arrange the angles to form a straight angle. b) "The angles opposite equal sides are equal." Exercise 1.3: Answers vary. These exercises could be followed in class under teacher supervision. Problem 2 a) prob. 1: 48, 143, 345 prob. 2: x= 134°, y = 46°, z=144° prob. 3: 155° prob. 4: 90° prob. 5: 35° prob. 6: mn = 40° prob. 6: a 29°, b = 145°, c = 85°. b) At least 12 different symbols were used for angles. Problem 3 prob. 35: x+90+200=360 (Zs at a point) x+290=360 x=70 200 prob. 36: Letx=ZUTR, y=ZQ.z = ∠PRQ, and w = ∠TRS. S y = 40 (base 4s of isos. A) 2+40+40180 (4 sum of A) z=100 w = 100 x = 100+20 x=120 (vert. 2s) (ext. of A) T to 20 U ૨ ૪ P 40 prob. 37: Let o∠CDE, p= ∠CED, and q∠CEA. A E D 30% B C o=p (bases of isos. A) 2p+30=180 (2 sum of A) p=75 q+75=180 (2s on a line) q = 105 m105 (opp. 4s //-ogram) Problem 4 a) True, by (2 sum of rt. A) b) False. The angle sum in a triangle is 180°, so the sum of any two angles in a triangle must be less than 180°. c) True. by (2s on a line) Problem 5 b) 105 x+35+105180 ( sum of A) x=40 35 d) x+58=32+90 (ext. of A) x=64 58 135 x+90135 (ext. 2 of 4) x=45 g) y = 56 (vert. 45) x+6856180 (2 sum of A) x+124180. x = 56 j) y+60=180 (Zs on a line) y = 120 x+120=90+60 (ext. 4 of A) x+120=150 x=30 Problem 6 b) c) 3x=x+58 (ext. & of A) 2x = 58 x = 29 a180-2x (s on a line) 4x=x+180-2x (ext. 2 of 4) 5x = 180 x = 36 الحه f) c180-3x (Zs on a line) 4x2x+180-3x (ext. of A) 5x180 x=36 C 3 g) m180-3x (Ls on a line) 3xx+180-3x (ext. 2 of A) 5x180 x=36 3 3° 3