SSA is not a valid congruence criterion

09 Mar
Class 10, Class 9 - Triangles, Math Concepts, Mathematics Theorems, Theorems, , , , ,

SSA is not a valid congruence criterion

Student: What is SSA?

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

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 🌓 of the money you save. 

You know… ⏰ Time is 💰 Money 😂 🤣 😆

If you still insist, written below is the explanation why SSA is not a valid congruence criterion. 🤿 👀 ❤️ 💃

But First, Let’s Sing it!!!

As I always say – Mathematics is like Music. Enjoy it!!! But don’t enjoy this one alone 🥳. This piece of music (SSA) is a party 🎉 song 🎶. So enjoy it with your friends. 💃🕺💃🕺. (I can’t ask in more creative 🎭 way to share 🔗 it. Hmmmmm… Let me say it clearly then… I BEG YOU. SHARE it pls. 😭 🙏 😭🙏 ) 

SSA – Sing Sing Aaaaaaaa….. 

SSA – Share Share Aaaaaaaa….. 

SSA – Subscribe Subscribe Aaaaaaaa….. 

Student – Sir, how about if we reverse the abbreviation 🤭 🙈 😆 🍑 🫏

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. 

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 triangles▲ABC and ▲ADC

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

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.