Greater Angle has the Greater Side Opposite to It
Here we will prove that if two angles of a triangle are unequal, the greater angle has the greater side opposite to it.
Given: In ∆XYZ, ∠XYZ > ∠XZY
To Prove: XZ > XY
Proof:
|
Statement 1. Let us assume that XZ is not greater than XY. Then XZ must be either equal to or less than XY. Let XZ = XY ⟹ ∠XYZ = ∠XZY 2. But ∠XYZ ≠ ∠XZY 3. Again, XZ < XY ⟹ ∠XYZ < ∠XZY 4. But ∠XYZ is not less than ∠XZY. 5. Therefore, XZ is neither equal to nor less than XY. 6. Therefore, XZ > XY. (Proved) |
Reason 1. Angles opposite to equal sides are equal. 2. Given, ∠XYZ > ∠XZY 3. The greater side of a triangle has the greater angle opposite to it. 4. Given that ∠XYZ > ∠XZY. 5. Both the assumptions are leading to contradictions. 6. From statement 5. |
Note: The side opposite to the greatest angle in a triangle is the longest.
From Greater Angle has the Greater Side 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.
Recent Articles
-
Converting Fractions to Decimals | Solved Examples | Free Worksheet
Apr 28, 25 01:43 AM
In converting fractions to decimals, we know that decimals are fractions with denominators 10, 100, 1000 etc. In order to convert other fractions into decimals, we follow the following steps: -
Expanded Form of a Number | Writing Numbers in Expanded Form | Values
Apr 27, 25 10:13 AM
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… -
Converting Decimals to Fractions | Solved Examples | Free Worksheet
Apr 26, 25 04:56 PM
In converting decimals to fractions, we know that a decimal can always be converted into a fraction by using the following steps: Step I: Obtain the decimal. Step II: Remove the decimal points from th… -
Worksheet on Decimal Numbers | Decimals Number Concepts | Answers
Apr 26, 25 03:48 PM
Practice different types of math questions given in the worksheet on decimal numbers, these math problems will help the students to review decimals number concepts. -
Multiplication Table of 4 |Read and Write the Table of 4|4 Times Table
Apr 26, 25 01:00 PM
Repeated addition by 4’s means the multiplication table of 4. (i) When 5 candle-stands having four candles each. By repeated addition we can show 4 + 4 + 4 + 4 + 4 = 20 Then, four 5 times
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.