HomeClass Notes1,200,000US530,000

MATH-UA 120 Lecture Notes - Lecture 13: Internal And External Angles, Triangle Inequality

22 views2 pages

7 Sep 2016

School

New York University

Department

Course

Professor

For unlimited access to Class Notes, a Class+ subscription is required.

Document Summary

Multiplication inequality postulate- if a0, then ac0 , then a/cb, or a=b. The measure of the exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. The measure of the exterior angle of a triangle is greater than the measure of either remote interior angle. The longest/middle/shortest side of a triangle is always opposite the largest/middle/smallest angle. The largest/middle/smallest angle of a triangle is always opposite the longest/middle/shortest side. Shortest distance from a point to a line: If you want to find the shortest distance from a point to a line, its through the segment perpendicular to the line.

Related textbook solutions

Calculus

ISBN: 9781319050733

Single Variable Calculus: Early Transcendentals

4th Edition, 2018

ISBN: 9781337687805

CALCULUS:EARLY TRANSCENDENTALS

ISBN: 9781319050740

Related Documents

MATH-UA 120 Lecture Notes - Lecture 4: Regular Polygon, Parallelogram, Hypotenuse

MATH-UA 120 Lecture Notes - Lecture 1: Bisection, Decimal Mark, Sexagesimal

MATH-UA 120 Lecture 10: Equality of Matrices

Related Questions

Two angles are said to be congruent if

A. The sum of their measures is 180

B. They share a side

C. They have the same angle measure

j

PLEASE NEED HELP WITH THIS TEST!!!

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.

mauvemuskrat666