Problem on Inequalities in Triangle

Here we will solve the problem on inequalities in triangle.

Let XYZ be a triangle in which XM bisects ∠YXZ. Prove that XY is greater than YM.

Problem on Inequalities in Triangle

Solution:

As XM bisects ∠YXZ, we have ∠YXZ = ∠MXZ ............ (i)

Also, in ∆XMZ, ∠XMY > ∠MXZ, as an exterior angle of a triangle is always greater then either of the interior opposite angles.

Therefore, ∠XMY > ∠YXM, [From (i)].

Therefore, XY > YM, as the greater angle has the greater side opposite to it.










9th Grade Math

From Problem on Inequalities in Triangle to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

  1. Worksheets on Comparison of Numbers | Find the Greatest Number

    Oct 10, 24 05:15 PM

    Comparison of Two Numbers
    In worksheets on comparison of numbers students can practice the questions for fourth grade to compare numbers. This worksheet contains questions on numbers like to find the greatest number, arranging…

    Read More

  2. Counting Before, After and Between Numbers up to 10 | Number Counting

    Oct 10, 24 10:06 AM

    Before After Between
    Counting before, after and between numbers up to 10 improves the child’s counting skills.

    Read More

  3. Expanded Form of a Number | Writing Numbers in Expanded Form | Values

    Oct 10, 24 03:19 AM

    Expanded Form of a Number
    We know that the number written as sum of the place-values of its digits is called the expanded form of a number. In expanded form of a number, the number is shown according to the place values of its…

    Read More

  4. Place Value | Place, Place Value and Face Value | Grouping the Digits

    Oct 09, 24 05:16 PM

    Place Value of 3-Digit Numbers
    The place value of a digit in a number is the value it holds to be at the place in the number. We know about the place value and face value of a digit and we will learn about it in details. We know th…

    Read More

  5. 3-digit Numbers on an Abacus | Learning Three Digit Numbers | Math

    Oct 08, 24 10:53 AM

    3-Digit Numbers on an Abacus
    We already know about hundreds, tens and ones. Now let us learn how to represent 3-digit numbers on an abacus. We know, an abacus is a tool or a toy for counting. An abacus which has three rods.

    Read More