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


Greater Side has the Greater Angle Opposite to it

Here we will prove that if two sides of a triangle are unequal, the greater side has the greater angle opposite to it.

Given: In ∆XYZ, XZ > XY

Greater Side has the Greater Angle Opposite to It

To prove: ∠XYZ > ∠XZY.

Construction: From XZ, cut off XP such that XP equals XY. Join Y and P.

Proof:

            Statement

1. In ∆XYP, ∠XYP = ∠XPY

2. ∠XPY = ∠XZY + ∠PYZ

            Reason

1. XY = XP

2. In ∆YPZ, exterior ∠XPY = Sum of interior opposite angles, ∠PZY (=∠XZY) and ∠PYZ.

3. Therefore, ∠XPY > ∠XZY.

4. Therefore, ∠XYP > ∠XZY.

5. But ∠XYZ > ∠ XYP.

6. Therefore, ∠XYZ > ∠XZY. (Proved)

3. From statement 2.

4. Using statements 1 in 3.

5. ∠XYZ = ∠XYP + ∠PYZ

6. Using statements 5 and 4.


Note: The angle opposite to the greater side in a triangle is the greatest in measure.






9th Grade Math

From Greater Side has the Greater Angle Opposite to It 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. 8 Times Table | Multiplication Table of 8 | Read Eight Times Table

    May 18, 25 04:33 PM

    Printable eight times table
    In 8 times table we will memorize the multiplication table. Printable multiplication table is also available for the homeschoolers. 8 × 0 = 0 8 × 1 = 8 8 × 2 = 16 8 × 3 = 24 8 × 4 = 32 8 × 5 = 40

    Read More

  2. Worksheet on Average | Word Problem on Average | Questions on Average

    May 17, 25 05:37 PM

    In worksheet on average interest we will solve 10 different types of question. Find the average of first 10 prime numbers. The average height of a family of five is 150 cm. If the heights of 4 family

    Read More

  3. How to Find the Average in Math? | What Does Average Mean? |Definition

    May 17, 25 04:04 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

  4. Problems Based on Average | Word Problems |Calculating Arithmetic Mean

    May 17, 25 03:47 PM

    Here we will learn to solve the three important types of word problems based on average. The questions are mainly based on average or mean, weighted average and average speed.

    Read More

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

    May 16, 25 11:13 AM

    Round off to Nearest One
    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