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MATH-UA 121 Lecture Notes - Lecture 8: Bisection, Angle

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22 Sep 2016

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If two angles are right angles, then they are congruent. If two angles are congruent, then their complements are congruent. If two angles are complimentary to the same angle, then they are congruent. Complements of the same angle are congruent. Supplements of the same angle are congruent. If two adjacent angles form a right angle, then they are complimentary. If two angles are vertical angles, then they are congruent. Vertical angles are congruent: triangle proofs. A triangle is the union of 3 line segments such that their endpoints are 3 non- collinear points. Congruent triangles are two triangles such that the 3 sides and 3 angles of one are congruent, respectively, to the 3 sides and 3 angles of the other. In notation, order is important, as each angle of one triangle is congruent to the respective angle of the other. The congruent parts are called corresponding parts.

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Use the figure below for Exercises 32-34. Find m 2 if mST = 132. Find m 4 if mRQT = 136. Find mQTS if m 1 = 27 and m 2 = 60. Classify the triangle as right, acute, or obtuse if the measures of its sides are 31, 45, and 56. Find the center and radius of the circle with equation (x + 6)2 + (x - 5)2 = 64. Find the lengths of MW- and MX-. Round your answers to the nearest tenth. Find the area of the trapezoid. Find the value of x if BD = 8 and BC = 17. Find the area of an equilateral triangle with perimeter of 60 in. Round your answer to the nearest hundredth. Find the values of x and y. Leave your answers in simplest radical form. The lengths of the sides of a right triangle are 18 ft. 24 ft. and 30 ft. What is the area of the triangle? 216 ft2 270 ft2 432 ft2 cannot be determined Find the volume of the cylinder in terms of pi. Find the value of x. Determine which of the following will tessellate. Decagon pentagon octagon triangle Determine the angle of rotation of Figure 1 to Figure 2. Figure 1 Figure 2 Given CKMS ~ DLNT. If the area of CKMS is 32 cm2, what is the area of DLNT? Find the height of a regular square prism with base edge of 6 ft and volume of 504 ft 3. What is the distance between (-12.6) and (8, -9)? Find the value of x. Assume that segments that appear to be tangent are tangent. 40 50 60 100 Find the values of x and y. If Delta DHT is similar to a triangle whose sides have lengths 4, 7, and 9. which of the following could be the perimeter of Delta DHT? 20 40 60 any of these Identify the hypothesis and conclusion of the conditional. If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. Which of the following is the converse of the conditional in Exercise 3? If a point is congruent from the endpoints of a segment, then it is on the perpendicular bisector of the segment. If a point is equidistant from a segment, then it is on a segment perpendicular to the bisector. If a point is not on the perpendicular bisector of a segment, then it is not equidistant from the endpoints of the segment. If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. What is the equation of a line perpendicular to that contains (4, -3)? 2x - y = 11 x - 2y = 10 2x - y = 5 x - 2y = -2 Find the length of BD. YW rightarrow bisects . Find m . Given Delta JKL ~ Delta MNP with a scale factor of 3 : 4. If Delta JKL has perimeter 57, what is the perimeter of Delta MNP? If Delta KLM Delta BCS, then which of the following is not true? Use the figure below for Exercises 10-13. Identify the pairs of angles as: alternate interior angles corresponding angles same-side interior angles vertical angles A circle has radius 17 m. Find its area and circumference to the nearest tenth. Find the coordinates of the midpoint of (9, 1) and (3, -5). Write the equation of a line in slope-intercept form that is parallel to y = - x + 8 and contains (-3 ,-5). For each pair of triangles, state the postulate or theorem you can use to prove the triangles congruent. If the triangles cannot he proven congruent, write not possible.

Show transcribed image text Use the figure below for Exercises 32-34. Find m 2 if mST = 132. Find m 4 if mRQT = 136. Find mQTS if m 1 = 27 and m 2 = 60. Classify the triangle as right, acute, or obtuse if the measures of its sides are 31, 45, and 56. Find the center and radius of the circle with equation (x + 6)2 + (x - 5)2 = 64. Find the lengths of MW- and MX-. Round your answers to the nearest tenth. Find the area of the trapezoid. Find the value of x if BD = 8 and BC = 17. Find the area of an equilateral triangle with perimeter of 60 in. Round your answer to the nearest hundredth. Find the values of x and y. Leave your answers in simplest radical form. The lengths of the sides of a right triangle are 18 ft. 24 ft. and 30 ft. What is the area of the triangle? 216 ft2 270 ft2 432 ft2 cannot be determined Find the volume of the cylinder in terms of pi. Find the value of x. Determine which of the following will tessellate. Decagon pentagon octagon triangle Determine the angle of rotation of Figure 1 to Figure 2. Figure 1 Figure 2 Given CKMS ~ DLNT. If the area of CKMS is 32 cm2, what is the area of DLNT? Find the height of a regular square prism with base edge of 6 ft and volume of 504 ft 3. What is the distance between (-12.6) and (8, -9)? Find the value of x. Assume that segments that appear to be tangent are tangent. 40 50 60 100 Find the values of x and y. If Delta DHT is similar to a triangle whose sides have lengths 4, 7, and 9. which of the following could be the perimeter of Delta DHT? 20 40 60 any of these Identify the hypothesis and conclusion of the conditional. If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. Which of the following is the converse of the conditional in Exercise 3? If a point is congruent from the endpoints of a segment, then it is on the perpendicular bisector of the segment. If a point is equidistant from a segment, then it is on a segment perpendicular to the bisector. If a point is not on the perpendicular bisector of a segment, then it is not equidistant from the endpoints of the segment. If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. What is the equation of a line perpendicular to that contains (4, -3)? 2x - y = 11 x - 2y = 10 2x - y = 5 x - 2y = -2 Find the length of BD. YW rightarrow bisects . Find m . Given Delta JKL ~ Delta MNP with a scale factor of 3 : 4. If Delta JKL has perimeter 57, what is the perimeter of Delta MNP? If Delta KLM Delta BCS, then which of the following is not true? Use the figure below for Exercises 10-13. Identify the pairs of angles as: alternate interior angles corresponding angles same-side interior angles vertical angles A circle has radius 17 m. Find its area and circumference to the nearest tenth. Find the coordinates of the midpoint of (9, 1) and (3, -5). Write the equation of a line in slope-intercept form that is parallel to y = - x + 8 and contains (-3 ,-5). For each pair of triangles, state the postulate or theorem you can use to prove the triangles congruent. If the triangles cannot he proven congruent, write not possible.

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Lines that form right angles at their point of intersection. A five-sided polygon. A round figure whose surface is at all points equidistant from the center. A geometric figure having three line segments for sides. A quadrilateral where each angle is a right angle. An equilateral parallelogram. The distance around a geometric figure. A segment with end points on the circle. A chord of a circle that contains the center of a circle. A segment joining the center of a circle to a point of the circle. Algebra A extremes B. graph C. numerical order D. range E ranking F. variable G. exponent H algebra A letter that is used in place of a numeral. The branch of mathematics that uses letters, called variables, in places of numerals. The n in X" indicating the number of factors of X. Data in order from smallest to largest or vice-versa. A pictorial representation of data. The two outer terms of a proportion. The difference between the greatest and least numbers in a list of data. Data organized in ascending or descending order. Practical Test Solve each problem below. You may use a piece of scratch paper to work your problems. You do not have to turn in your work sheet. Write only the answer in the space provided for each question. Write the number for six million, four hundred thousand, nine hundred twenty seven. _____________________________________ Robert bought a used automobile for $1, 500.00. If the sales tax is 5%, what will be the total that Robert had to pay for the automobile? __________________ Solve 2/3 + 4/6 ______________ What is the perimeter of a triangle which sides measure 6, 8, and 10 inches? _________________ What would be the radius of a circle with a diameter of 8 inches? _________________ Solve 2x + 3 = 9, x= ____________ What is the area of a rectangle with a width of 12 feet and a length of 10 feet? ____________ Using the fraction 4/6, which number is the denominator? _____________ What percent of one U.S. dollar is $.25? ____________ Tom, Bill, Susan, and Sandy went bowling. Tom's score was 132, Bill's score was 140, Susan's scored 145 and sandy's score was 128. What was the average score of all four bowlers? __________ A dress that sells for $50.00 now has a 10% discount marked on the tag. How much will you save off the regular price of the dress? ____________ Sam bought a pair of socks for $2.95 and a tie for $7.50. He gave the cashier a twenty dollar bill. How much change should Sam receive from the cashier? _____________ A cube measures 3 inches on all of it's sides. What is the volume of the cube in inches? ______________ Canned corn is on sale at the grocery store, three cans for a dollar. Another brand is only $.30 per can, which is the better buy? ____________ Your paycheck each week is $500.00. If you want to save $2,000.00 dollars in one year, how much should you set aside from your paycheck each week? _______________