University:
South Plains College
Course:
MATH 1332 | Contemporary Mathematics
Academic year:

2024
Views:

480

Pages:

9
Author:

Alexia V.

Name MATH 1332 Notes 3.1 MATH 0332/1332 Notes 4.1 Angles, Curves and Polygons Angles Definition: Two angles that add up to 90 degrees are called complementary angles. Definition: Two angles that add up to l80 degrees are called supplemcntary angles. Give the measure of the complement of cach angle. 1. 70° x40 70 3. (x + 30)° 2. 43º q0-(x+3) q0-43. 47° -70 q0-x -30 Give the measure of the supplement of each angle. 6. (x + 30)° 5. 43° 4. 70° 18-43 Definition; Pair angles formed when two lines intersect are called vertical angles. Vertical angles have the same measurement. i20 B Find the measure of each marked angle. 7. 75)+l7- 9 8 (7x + 17)° 710) -2o (5x)° -7x 2 -7y 2 7x-20) -7y Definition: An angle that measure 180 degrees is called a straight angle. Definition: Alinear pair of angles is a pair of adjacent, supplementary angles. B m<1+ m< 2=180° Find the measure of each marked angle. -46)+ 9. 7(22)-96 D (7q-46)/(3q+6)" B 14 4 10. F6 =180 22° 2(38)+S1 (2x +5)A (4y -1) K(3x -33) 3C38)-3) 2x+S 3y-33 -2 +>) Polvgons Definition: Asimple curve is acurve that can be drawn without lifing your pen/pencil and without passing through any point twice. Definition: Acloscd curve is acurve that can be drawn without lifting your pen/pencil in which the þeginning and ending points are the same. Deinition: Apolygon is asimple, closed curve made up of only line segments. The lines segments are alled sidcs and the points at which the sides meet are called vertices. Pehygons Net palygns Definition:A polygon is said to be convex if, for any two points inside the figure, the lines segment bonnecting the two points is completely inside the figure. pefinition: Apolygon is said to be concave if it is not convex. Convex Polygons Concave Polygons (Not Convex) A polygon is named by the mumber of sides that it has. Name Number of Sides Triangle 3 Quadrilateral 4 Pentagon 5 6 Hexagon Heptagon Octagon Nonagon 9 Decagon 10 pefinition: Aregular polygon is apolygon in which allangles are equal and all sides are equal. Regular Triangle Non-Regular Triangles Regular Quadrilateral Non-Regular Quadrilaterals Regular Pentagon Classifving Triangles Equilateral Triangle Allthree sides are the same length. Non-Regular Pentagons Classifving Triangles by Sides Isosceles Triangle At least two of the three sides are the same length. Note: Since all three sides are the same length, all three angles of the triangle will be the same measure. Note: Since two sides are the same length, two angles of the triangle will be the same megsure. Scalene Triangle No sides are the same length. Note: Since there are three different side lengths, then each angle will have a different measure. Classifying Triangles by Angles Allthree angles are acute angles (less than 90°). Obtuse Triangle Right Triangle Acute Triangle There will be one angle that is a right angle (90° angle). There will be one angle that is an obtuse angle (more than 90°). Classify the triangle shown by both sides and angles. 12. 11. 5 cm/ 3 in Scalene, kigh TSoscde Acute 14. 13. 115° 4 in Iso5uts obtuse Scalen,sotse 16. 15. Aote keral, Equla (Als0 Isosties, Pigh Propertiesof Triangles Angle Sum Theorem: The sum of the measure of the three interior angles of any triangle is 180°. m170 34 1 Exterior Angle Theorem: The measure of an exterior angle measures of thetwo opposite interior angles. of a triangle is equal to the sum of the I30 136 m<4= m<2+ m<3 19. Find the measure of the exterior angle indicated below. 3C00)-40=4o -(x + 20)° (3x - 40)° angle EDK as well as the measure 20. Find the measure of exterior and angle EDF) for the triangle shown. +19= 5y-$ t60 14 600 3x=3b /5x-5 E D 8x+ 19 of the missing interior angles (angle E 3 3 Common Types off Quadrilaterals: Name Picture Information A quadrilateral with exactly one pair of parallel sides. base Trapezoid leg leg base Rectangle A quadrilateral in which all interior angles are right angles (measure 90°). Note: Since all of the angle measures are 90°, then opposite sides of the rectangle are congruent. Parallelogram Aquadrilateral in which opposite sides are parallel. Note: Since opposite sides are parallel, then opposite angles are cOngruent and opposite sides will also be congruent. Square Rhombus Aquadrilateral with four equal sides and four right angles. paralelogram with four equal A sides lengths. a square is also Note that some quadrilaterals can be classified in more than one category. For example, a rhombus, a rectangle, and parallelogram. Angle Sum Theorem: The sum of the measure of the four interior angles of any quadrilateral is 360°. Circles pefinition: A ircle is the set of all is called the çenter and þoint points in a plane that are that distance is called the radius.cquidistant from a fixed point. That fixe center radius hafnition: Thediameter of a circle is the length ofa line segment through the center of the circle endnoints that are on the circle. The diameter is double the length of the radius. radius diameter