math concepts Archives – Mathemafia https://mathemafia.com/tag/math-concepts/ Mathematics is like music - Enjoy it!!! Tue, 25 Mar 2025 09:11:45 +0000 en-US hourly 1 https://wordpress.org/?v=7.1 https://mathemafia.com/wp-content/uploads/2020/08/cropped-M__Logo__SM-1-32x32.png math concepts Archives – Mathemafia https://mathemafia.com/tag/math-concepts/ 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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