1 / 41

TMAT 103

TMAT 103. Chapter 2 Review of Geometry. TMAT 103. § 2.1 Angles and Lines. § 2.1 – Angles and Lines. A right angle measures 90 . § 2.1 – Angles and Lines. An acute angle measures less than 90 . § 2.1 – Angles and Lines. An obtuse angle measures more than 90 .

ryee
Télécharger la présentation

TMAT 103

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. TMAT 103 Chapter 2 Review of Geometry

  2. TMAT 103 §2.1 Angles and Lines

  3. §2.1 – Angles and Lines • A right angle measures 90

  4. §2.1 – Angles and Lines • An acute angle measures less than 90

  5. §2.1 – Angles and Lines • An obtuse angle measures more than 90

  6. §2.1 – Angles and Lines • Two vertical angles are the opposite angles formed by two intersecting lines • Two angles are supplementary when their sum is 180 • Two angles are complementary when their sum is 90

  7. §2.1 – Angles and Lines • Angles p and q are vertical, as are m and n • Angles p and n are supplementary, as are angels m and q

  8. §2.1 – Angles and Lines • 2 lines are perpendicular when they form a right angle • The shortest distance between a point and a line is the perpendicular distance between them

  9. §2.1 – Angles and Lines • Two lines are parallel if they lie in the same plane and never intersect • If two parallel lines are intersected by a third line (called a transversal), then • Alternate interior angles are equal • Corresponding angles are equal • Interior angles on the same side of the transversal are supplementary

  10. §2.1 – Angles and Lines • a and g are equal (alternate interior) • a and e are equal (corresponding) • a + f = 180 

  11. TMAT 103 §2.2 Triangles

  12. §2.2 – Triangles • A polygon is a closed figure whose sides are all line segments • A triangle is a polygon with 3 sides

  13. §2.2 – Triangles • Types of triangles • Scalene – no 2 sides are equal • Isosceles – 2 sides are equal • Equilateral – all 3 sides are equal

  14. §2.2 – Triangles • Types of triangles • Acute – all 3 angles are acute • Obtuse – one angle is obtuse • Right – one angle is 90 

  15. §2.2 – Triangles • In a right triangle, the side opposite the right angle is the hypotenuse, and the other two sides are the legs • Pythagorean Theorem: The square of the hypotenuse of a right triangle is equal to the sum of the squares of the 2 legs

  16. §2.2 – Triangles • The median of a triangle is the line segment joining any vertex to the midpoint of the opposite side

  17. §2.2 – Triangles • The altitude of a triangle is a perpendicular line segment from any vertex to the opposite side

  18. §2.2 – Triangles • An angle bisector of a triangle is a line segment that bisects any angle and intersects the opposite side

  19. §2.2 – Triangles • The sum of the interior angles of any triangle is 180 • In a 30 – 60 – 90 triangle • The side opposite the 30 angle equals ½ the hypotenuse • The side opposite the 60 angle equals times the length of the hypotenuse

  20. §2.2 – Triangles • Perimeter and Area • Perimeter – distance around • The area of a triangle is ½ the base times the height • A = ½ bh • Heron’s Formula • When only the 3 sides of a triangle are known

  21. §2.2 – Triangles • Triangles are similar () if their corresponding angles are equal or if their corresponding sides are in proportion

  22. §2.2 – Triangles • Triangles are congruent () if their corresponding angles and sides are equal

  23. TMAT 103 §2.3 Quadrilaterals

  24. §2.3 – Quadrilaterals • A quadrilateral is a polygon with 4 sides • A parallelogram is a quadrilateral having 2 pairs of parallel sides

  25. §2.3 – Quadrilaterals • The area of a parallelogram is the base times the height • A = bh • The opposite sides and opposite angles of a parallelogram are equal

  26. §2.3 – Quadrilaterals • The diagonal of a parallelogram divides it into 2 congruent triangles • The diagonals of a parallelogram bisect each other

  27. §2.3 – Quadrilaterals • A rectangle is a parallelogram with right angles • A square is a rectangle with equal sides • A rhombus is a parallelogram with equal sides

  28. §2.3 – Quadrilaterals • A trapezoid is a quadrilateral with only one pair of parallel sides • The area of a trapezoid is given by the formula:

  29. TMAT 103 §2.4 Circles

  30. §2.4 – Circles • A circle is the set of all points on a curve equidistant from a given point called the center • A radius is the line segment joining the center and any point on the circle • A diameter is the chord passing through the center • A tangent is a line intersecting a circle at only one point • A secant is a line intersecting a circle in two points • A semicircle is half of a circle

  31. §2.4 – Circles • Circle terminology

  32. §2.4 – Circles • The area of a circle is given by: • A = r2 • r is the radius • The circumference of a circle is given by either of the following: • C = 2r • r is the radius • C = d • d is the diameter

  33. §2.4 – Circles • Circular Arcs • A central angle is formed between 2 radii and has its vertex at the center of the circle • An inscribed angle has vertex on the circle and sides are chords • An arc is the part of the circle between the 2 sides of a central or inscribed angle • The measure of an arc is equal to • the measure of the corresponding central angle • twice the measure of the corresponding inscribed angle

  34. §2.4 – Circles • Example of central and inscribed angles

  35. §2.4 – Circles • Measurement relationships

  36. §2.4 – Circles • An angle inscribed in a semicircle is a right angle

  37. §2.4 – Circles • Find the measure of the blue arc

  38. §2.4 – Circles • A line tangent to a circle is perpendicular to the radius at the point of tangency

  39. TMAT 103 §2.5 Areas and Volumes of Solids

  40. §2.5 – Areas and Volumes of Solids • The lateral surface area of a solid is the sum of the areas of the sides excluding the area of the bases • The total surface area of a solid is the sum of the lateral surface area plus the area of the bases • The volume of a solid is the number of cubic units of measurement contained in the solid

  41. §2.5 – Areas and Volumes of Solids • In the following figures, B = area of base, r = length of radius, and h = height

More Related