Subscribe to our YouTube channel for the latest videos, updates, and tips.


Points on the Base of an Isosceles Triangle

Here we will prove that if two given points on the base of an isosceles triangle are equidistant from the extremities of the base, show that they are also equidistant from the vertex.

Solution:

Given: In the isosceles ∆XYZ, XY = XZ, M and N points on the base YZ such that YM = NZ.

Base of an Isosceles Triangle

To prove: XM = XN.

Proof:

          Statement

1. In ∆XYM and ∆XNZ,

(i) XY = XZ.

(ii) YM = NZ.

(iii) ∠XYM = ∠XZN.


2. Therefore, ∆XYM ≅ ∆XNZ.

3. XM = XN. (Proved).

            Reason

1.

(i) Given.

(ii) Given.

(iii) Angles opposite to equal sides XY and XZ.


2. By SAS criterion.

3. CPCTC.




9th Grade Math

From Points on the Base of an Isosceles 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

RSS

  1. How to Find the Average? | What Does Average Mean? | Definition

    May 15, 25 06:05 PM

    Average 2
    Average means a number which is between the largest and the smallest number. Average can be calculated only for similar quantities and not for dissimilar quantities.

    Read More

  2. Worksheet on Rounding Off Number | Rounding off Number | Nearest 10

    May 15, 25 05:12 PM

    In worksheet on rounding off number we will solve 10 different types of problems. 1. Round off to nearest 10 each of the following numbers: (a) 14 (b) 57 (c) 61 (d) 819 (e) 7729 2. Round off to

    Read More

  3. Worksheet on Rounding Decimals | Questions Related to Round a Decimal

    May 15, 25 11:52 AM

    Worksheet on Rounding Decimals
    The worksheet on rounding decimals would be really good for the students to practice huge number of questions related to round a decimal. This worksheet include questions related

    Read More

  4. Rounding Decimals | How to Round a Decimal? | Rounding off Decimal

    May 14, 25 03:01 PM

    Rounding decimals are frequently used in our daily life mainly for calculating the cost of the items. In mathematics rounding off decimal is a technique used to estimate or to find the approximate

    Read More

  5. Rounding Off to the Nearest Whole Number | Nearest 10, 100, and 1000

    May 13, 25 03:43 PM

    Nearest Ten
    Here we will learn how to rounding off to the nearest whole number?

    Read More