congruence Archives – Mathemafia http://sh016.global.temp.domains/~mathemaf/tag/congruence/ Mathematics is like music - Enjoy it!!! Tue, 25 Mar 2025 09:11:45 +0000 en-US hourly 1 https://wordpress.org/?v=7.0 https://mathemafia.com/wp-content/uploads/2020/08/cropped-M__Logo__SM-1-32x32.png congruence Archives – Mathemafia http://sh016.global.temp.domains/~mathemaf/tag/congruence/ 32 32 SSA is not a valid congruence criterion https://mathemafia.com/ssa-is-not-a-valid-congruence-criterion/ Sun, 09 Mar 2025 12:17:43 +0000 https://mathemafia.com/?p=13890 A witty explanation and proof by mathemafia that SSA is not a valid congruence criterion when it comes to the congruence of triangles in geometry.

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SSA is not a valid congruence criterion

Student: What is SSA?

Mathemafia – I call it Side Side Aaaaaaaaaa…..hhhhhhΒ !!!

Not funny, huh!! But effective 🎯 enough to remember 🧠.

If you want to read, it may take 5 minutes. If you want to save time, watch the short video and then send me half πŸŒ“ of the money you save.Β 

You know… ⏰ Time is πŸ’° Money πŸ˜‚ 🀣 πŸ˜†

If you still insist, written below is the explanation why SSA is not a valid congruence criterion. 🀿 πŸ‘€ ❀️ πŸ’ƒ

But First, Let’s Sing it!!!

As I always say – Mathematics is like Music. Enjoy it!!! But don’t enjoy this one alone πŸ₯³. This piece of music (SSA) is a party πŸŽ‰ song 🎢. So enjoy it with your friends. πŸ’ƒπŸ•ΊπŸ’ƒπŸ•Ί. (I can’t ask in more creative 🎭 way to share πŸ”— it. Hmmmmm… Let me say it clearly then… I BEG YOU. SHARE it pls. 😭 πŸ™ πŸ˜­πŸ™ )Β 

SSA – Sing Sing Aaaaaaaa…..Β 

SSA – Share Share Aaaaaaaa…..Β 

SSA – Subscribe Subscribe Aaaaaaaa…..Β 

StudentΒ – Sir, how about if we reverse the abbreviation 🀭 πŸ™ˆ πŸ˜† πŸ‘ 🫏

Mathemafia – Wow!!! That’s much more creative. 🫏 🫏 

Explanation

Let us draw an obtuse angled triangle, ABC with obtuse angle at vertex A as shown in the Pic 1.

Obviously side BC will be the longest side.Β 

Side opposite to largest angle is the longest side in a triangle.

Pic 1
Pic 2

Take a compass and draw an arc of length AB. It will intersect the longest side BC, say at point D.

See Pic 2.

Join AD.

Let us now focus on two trianglesβ–²ABC and β–²ADC

\( \begin{aligned} \overline{AB} &\cong \overline{AD} \ \ (Construction) \\ \overline{AC} &\cong \overline{AC} \ \ (Common) \\ \angle C &= \angle C \ \ (Common) \end{aligned}\)

So we got two congruent sides and one congruent angle in SSA formation but clearly the two triangles are not congruent. Hence, SSA is not a valid congruent criterion.Β 

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]]> Axioms – Lines and Angles https://mathemafia.com/axioms-lines-and-angles/ Thu, 18 Feb 2021 08:52:43 +0000 http://sh016.global.temp.domains/~mathemaf/?p=6299 Class 9 | Chapter 6 | Axiom 6.1, 6.2, 6.3, 6.4 | Mathematics NCERT This is a video tutorial that covers the following: Definitions of axiom Ray Line Line segment and their representation Adjacent angles Corresponding angles. Axiom 6.1 –Β If…

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Class 9 | Chapter 6 | Axiom 6.1, 6.2, 6.3, 6.4 | Mathematics NCERT

This is a video tutorial that covers the following:

  • Definitions of axiom
  • Ray
  • Line
  • Line segment and their representation
  • Adjacent angles
  • Corresponding angles.

Axiom 6.1 –Β If a ray stands on a line, then the sum of the two adjacent angles so formed is 180 degrees.

Axiom 6.2 – If the sum of two adjacent angles is 180 degrees, then the non common arms of the angles form a straight line.

Axiom 6.3 – If a transversal intersects two parallel lines, then each pair of corresponding angles are equal. (Corresponding Angles axiom)

Axiom 6.4 – If a transversal intersects two lines, such that a. pair of corresponding angles are equal, then the two lines are parallel. (Corresponding angles converse axiom)

Β 

Class 9 | Home

Chapter 6 – Lines and Angles

Mathemafia Logo - 75 px=> Axioms – Lines and Angles

This playlist covers all the questions, concepts, theorems and examples of chapter 6 (Lines and Angles) of class 9, NCERT textbook. Click a thumbnail to watch the tutorial.Β 

Watch complete chapter on YouTube
​

Theorems

Theorem 6.1

Theorem 6.2

Theorem 6.3

Theorem 6.4

Theorem 6.5

Theorem 6.6

Theorem 6.7

Theorem 6.8

Exercise 6.1

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Exercise 6.2

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Exercise 6.3

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Examples

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Example 8

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]]> CPCT or CPCTC https://mathemafia.com/cpct-or-cpctc/ Thu, 18 Feb 2021 08:16:42 +0000 http://sh016.global.temp.domains/~mathemaf/?p=6288 In NCERT books for class 9 and 10, term CPCT is used while proving congruence of triangles or other shapes. Very frequently students ask me this query why I use CPCTC instead of CPCT. The term CPCTC is more accurate…

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In NCERT books for class 9 and 10, term CPCT is used while proving congruence of triangles or other shapes. Very frequently students ask me this query why I use CPCTC instead of CPCT.

The term CPCTC is more accurate and right term because when we say CPCT that means Corresponding Parts of Congruent Triangles. Now, one question that should come to your mind is –

Corresponding Parts of Congruent Triangles – are what?

And we know that the answer is very simple – CONGRUENT.

Hence, CPCTC is more accurate term which means –

Corresponding Parts of Congruent Triangles are Congruent.

Recommended - Axioms (Lines & Angles)
Class 9 | Home

Chapter 6 – Lines and Angles

Mathemafia Logo - 75 px=> Axioms – Lines and Angles

This playlist covers all the questions, concepts, theorems and examples of chapter 6 (Lines and Angles) of class 9, NCERT textbook. Click a thumbnail to watch the tutorial.Β 

Watch complete chapter on YouTube
​

Theorems

Theorem 6.1

Theorem 6.2

Theorem 6.3

Theorem 6.4

Theorem 6.5

Theorem 6.6

Theorem 6.7

Theorem 6.8

Exercise 6.1

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Exercise 6.2

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Exercise 6.3

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Examples

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Example 8

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