Geometry Archives – Mathemafia

SSA is not a valid congruence criterion

Sunil Kumar — Sun, 09 Mar 2025 12:17:43 +0000

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.

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.

The post SSA is not a valid congruence criterion appeared first on Mathemafia.

Class 10 | Chapter 6 | All Solutions | Triangles

Sunil Syal — Fri, 17 Dec 2021 07:38:09 +0000

This playlist covers all the questions, concepts and examples of chapter 6 (Triangles) of class 10, NCERT book. Click a thumbnail to watch the tutorial.

Watch complete chapter on YouTube

Activity 2 – Chapter 6 | Class 10 | Triangles | NCERT Maths | CBSE

Theorem 6.1 – Basic Proportionality (Thales) Theorem, Class 10, Ch 6, Triangles | NCERT Maths | CBSE

Activity 3 – Chapter 6 | Class 10 | Triangles | NCERT Maths | CBSE

Theorem 6.2 – Converse of Basic Proportionality (Thales) Theorem, Class 10, Ch 6, Triangles | NCERT

Example 1 – Chapter 6 – Class 10 | Triangles | NCERT Maths | CBSE

Example 2 – Chapter 6 – Class 10 | Triangles | NCERT Maths | CBSE

Example 3 – Chapter 6 – Class 10 | Triangles | NCERT Maths | CBSE

Theorem 6.3 🥳 🤠 👏 AAA or AA triangles similarity theorem, Class 10, Ch 6, Triangles | NCERT

Theorem 6.4 – SSS similarity criterion of triangles theorem, Class 10, Ch 6, Triangles | NCERT

Theorem 6.5 – SAS similarity criterion of triangles theorem, Class 10, Ch 6, Triangles | NCERT

Example 4 – Chapter 6 – Class 10 | Triangles | NCERT Maths | CBSE

🔥🔥 Example 5 – Chapter 6 – Class 10 🔥🔥 Triangles | NCERT Maths | CBSE 💁👌😍

Example 6 – Chapter 6 – Class 10 | Triangles | NCERT Maths | CBSE

Example 7 – Chapter 6 – Class 10 | Triangles | NCERT Maths | CBSE

Example 7 – Chapter 6 – Class 10 ( Solution No: 2) | Triangles | NCERT Maths | CBSE

Example 8 – Chapter 6 – Class 10 | Triangles | NCERT Maths | CBSE

Example 8 (Another Easy solution for Part 3) – Chapter 6 – Class 10 | Triangles | NCERT Maths | CBSE

The post Class 10 | Chapter 6 | All Solutions | Triangles appeared first on Mathemafia.

Class 9 | Chapter 9 | All Solutions | Circles

Sunil Syal — Thu, 16 Dec 2021 15:35:31 +0000

This playlist covers all the questions, concepts, theorems and examples of chapter 10 (Circles) of class 9, NCERT textbook. Click a thumbnail to watch the tutorial.

Watch complete chapter on YouTube

Theorem 9.1 Class 9 | Chapter 9 | Circles | Equal chords subtend equal angles | NCERT Maths

Theorem 9.2 Class 9 | Chapter 9 | Circles, Equal angles by chords means equal chords | NCERT Maths

Class 9 | Chapter 10 | Circles | Introduction to circles and basic definitions | NCERT Maths

Question 1 Exercise 9.1 Class 9 | Chapter 9 | Circles | solution | NCERT Maths

Question 2 Exercise 9.1 Class 9 | Chapter 9 | Circles | solution | NCERT Maths

Theorem 9.3 Class 9 | Chapter 9 | Circles Perpendicular from the centre to a chord | NCERT Maths

Theorem 9.4 Class 9 | Chapter 9 | Circles – Proof | NCERT Maths | CBSE board

Theorem 10.5 Class 9 | Chapter 10 | Circles 💁👌😍 Circle through three non collinear points

Theorem 9.5 Class 9 | Chapter 9 | Circles – Equal chords are equidistant from centre | NCERT Maths

Theorem 9.6 Class 9 | Chapter 9 | Circles – Chords equidistant from centre are equal | NCERT Maths

Example 1 Chapter 9 Class 9 | Circles – Solved | NCERT Maths | CBSE board

🔥🔥 Question 1 Exercise 9.2 Class 9 | Chapter 9 💁👌😍 Circles | Solved | NCERT Maths CBSE board

Question 2 Exercise 9.2 Class 9 | Chapter 9 | Circles | Solved | NCERT Maths CBSE board

Question 3 Exercise 9.2 Class 9 | Chapter 9 | Circles | Solved | NCERT Maths CBSE board

Question 4 Exercise 9.2 Class 9 | Chapter 9 | Circles | Solved | NCERT Maths CBSE board

Question 5 Exercise 9.2 Class 9 | Chapter 9 | Circles | Solved | NCERT Maths CBSE board

Question 6 Exercise 9.2 Class 9 | Chapter 9 | Circles | Solved | NCERT Maths CBSE board

Theorem 9.7 Class 9 | Chapter 9 | Circles – Angle subtended by an arc at the centre | NCERT Maths

Theorem 9.8 Class 9 | Chapter 9 | Circles – Angles in the same segment of a circle are equal

Angle in a semicircle is a right angle | NCERT Class 9 Maths | Chapter 10, Circles

Theorem 9.9 Class 9 | Ch 9 | Circles – Line segment subtending equal angles and concyclic points

Theorem 9.10 Class 9 | Ch 9 | Circles – Sum of opposite pair of cyclic quadrilateral is 180 degrees

Theorem 9.11 Class 9 Circles – Sum of pair of opposite angles of quadrilateral is 180, it's cyclic

💁👌😍 Example 2 Chapter 9 Class 9 | Maths, Circles chapter solved | NCERT Maths

Example 3 Chapter 9 Class 9 | Maths | Circles explained | NCERT Maths

Example 5 Chapter 9 Class 9 | Circles | Maths – Solved & explained | NCERT Maths

Question 1 Exercise 9.3 Class 9 | Chapter 9 | Circles | Solved | NCERT Maths CBSE board

Question 2 Exercise 9.3 Class 9 | Chapter 9 | Circles | Solved | NCERT Maths CBSE board

Question 3 Exercise 9.3 Class 9 | Chapter 9 | Circles | Solved | NCERT Maths CBSE board

Question 4 Exercise 9.3 Class 9 | Chapter 9 | Circles | Solved | NCERT Maths CBSE board

Question 5 Exercise 9.3 Class 9 | Chapter 9 | Circles | Solved | NCERT Maths CBSE board

Question 6 Exercise 9.3 Class 9 | Chapter 9 | Circles | Solved | NCERT Maths CBSE board

Question 7 Exercise 9.3 Class 9 | Chapter 9 | Circles | Solved | NCERT Maths CBSE board

Question 8 Exercise 9.3 Class 9 | Chapter 9 | Circles | Solved | NCERT Maths CBSE board

Question 9 Exercise 9.3 Class 9 | Chapter 9 | Circles | Solved | NCERT Maths CBSE board

Question 10 Exercise 9.3 Class 9 | Chapter 9 | Circles | Solved | NCERT Maths CBSE board

Question 11 Exercise 9.3 Class 9 | Chapter 9 | Circles | Solved | NCERT Maths CBSE board

Question 12 Exercise 9.3 Class 9 | Chapter 9 | Circles | Solved | NCERT Maths CBSE board

Equal Or Congruent ? Lines and Angles

Question 5 Exercise 9.2 Class 9 🔥 Dubbed in Eng 🔥 Circles | Solved | NCERT Maths CBSE board

Proof – Angles in the same segment of a circle are equal – in English and 10+ languages

The post Class 9 | Chapter 9 | All Solutions | Circles appeared first on Mathemafia.

Class 9 | Chapter 8 | All Solutions | Quadrilaterals

Sunil Syal — Thu, 16 Dec 2021 15:34:22 +0000

This playlist covers all the questions, concepts, theorems and examples of chapter 8 (Quadrilaterals) of class 9, NCERT textbook. Click a thumbnail to watch the tutorial.

Watch complete chapter on YouTube

Theorem 8.1, chapter 8 Class 9, Diagonal of a parallelogram divides it into two congruent triangles

Section 8.2, Class 9 – Angle sum property of quadrilateral | Sum of angles is 360 degrees

Theorem 8.2 chapter 8 class 9 | Prove that opposite sides of a parallelogram are of equal length

Theorem 8.3, ch 8 Class 9, Pair of opposite sides of quadrilateral is equal, it's a parallelogram

Equal Or Congruent ? Lines and Angles

Theorem 8.4, chapter 8 Class 9, How to prove that opposite angles of a parallelogram are congruent

Theorem 8.5, ch 8 Class 9, Pair of opposite angles of quadrilateral is equal, it's a parallelogram

Theorem 8.6, ch 8 Class 9, How to prove that the diagonals of a parallelogram bisect each other

Theorem 8.7, ch 8 Class 9, Diagonals of quadrilateral bisect each other, then it's a parallelogram

Class 9 | Chapter 8 | Example 1 Explanation | NCERT| Quadrilaterals – Each angle of rectangle is 90°

Example 2, Chapter 8, Class 9 – Diagonals of a square / rhombus are perpendicular to each other

Class 9 | Chapter 8 | Example 3 Explanation | NCERT| Quadrilaterals

Class 9 | Chapter 8 | Example 4 Explanation | NCERT| Quadrilaterals

Class 9 | Chapter 8 | Example 5 Explanation | NCERT Maths | Quadrilaterals

Theorem 8.8, Class 9, A pair of opp sides of quadrilateral is equal+parallel ⇒ it's a parallelogram

Question 1, Exercise 8.1, Ch 8, Class 9 | Parallelogram's diagonal are equal, then it's a rectangle

Question 2, Exercise 8.1, Ch 8, Class 9 | Diagonals of square are equal, bisect at right angles

Question 3, Exercise 8.1, Ch 8, Class 9 | Diagonal of parallelogram bisect the angles | Rhombus

Question 4, Ex 8.1, Ch 8, Class 9, Diagonal of rectangle bisects opposite angles, it is square

Question 5, Exercise 8.1, Ch 8, Class 9 Maths | Questions on Parallelograms and Congruent Triangles

Question 6, Exercise 8.1, Ch 8, Class 9 Maths | Questions on Parallelograms and Congruent Triangles

Question 7, Exercise 8.1, Ch 8, Class 9 Maths | Ques on Trapezium, Parallelogram, Congruent Triangle

Theorem 8.9 Chapter 8 Class 9 | MID POINT THEOREM | Proof in 2 different ways

Theorem 8.10 Chapter 8 Class 9 | CONVERSE OF MID POINT THEOREM | Proved by 3 different methods

Class 9 | Chapter 8 | Example 6 Explanation | NCERT Maths | Quadrilaterals

Class 9 | Chapter 8 | Example 7 Explanation | NCERT Maths | Quadrilaterals

Question 1 Exercise 8.2 Chapter 8 Class 9 | Proof | NCERT | Quadrilaterals

Question 2 Exercise 8.2 Chapter 8 Class 9 | Proof | NCERT | Quadrilaterals

Question 3 Exercise 8.2 Chapter 8 Class 9 | Proof | NCERT | Quadrilaterals

Question 4 Exercise 8.2 Chapter 8 Class 9 | Proof | NCERT | Quadrilaterals

Question 5 Exercise 8.2 Chapter 8 Class 9 | Proof | NCERT | Quadrilaterals

Question 6 Exercise 8.2 Chapter 8 Class 9 | Proof | NCERT | Quadrilaterals

The post Class 9 | Chapter 8 | All Solutions | Quadrilaterals appeared first on Mathemafia.

Class 9 | Chapter 7 | All Solutions | Triangles

Sunil Syal — Thu, 16 Dec 2021 15:34:06 +0000

This playlist covers all the questions, concepts, theorems and examples of chapter 7 (Triangles) of class 9, NCERT textbook. Click a thumbnail to watch the tutorial.

Watch complete chapter on YouTube

Class 9 | Chapter 7 | Example 1 Explanation | NCERT| Congruent Triangles

Congruence v/s Similarity – Explanation of difference between Congruent and Similar with examples

Example 2 – Chapter 7 – Class 9 – Proof of the perpendicular bisector theorem

Class 9 | Chapter 7 | Theorem 7.1 Proof of ASA (Angle Side Angle) Congruence rule | NCERT Maths

Class 9 | Chapter 7 | Example 3 Explanation | NCERT| Congruent Triangles

Class 9 | Chapter 7 | Exercise 7.1, Question 1 Proof | NCERT| Congruent Triangles

Class 9 | Chapter 7 | Exercise 7.1, Question 2 Proof | NCERT| Congruent Triangles

Class 9 | Chapter 7 | Exercise 7.1, Question 3 Proof | NCERT| Congruent Triangles

Class 9 | Chapter 7 | Exercise 7.1, Question 4 Proof | NCERT| Congruent Triangles

Class 9 | Chapter 7 | Exercise 7.1, Question 5 Proof | NCERT| Congruent Triangles

Class 9 | Chapter 7 | Exercise 7.1, Question 6 Proof | NCERT| Congruent Triangles

Class 9 | Chapter 7 | Exercise 7.1, Question 7 Proof | NCERT| Congruent Triangles

Class 9 | Chapter 7 | Exercise 7.1, Question 8 Proof | NCERT| Congruent Triangles

Theorem 7.2, Chapter 7, Class 9 – Isosceles triangle theorem – Proof (by 2 different methods)

Theorem 7.3, Chapter 7, Class 9 – Proof | Converse of Isosceles triangle theorem

Class 9 | Chapter 7 | Example 4 Explanation | NCERT| Congruent Triangles

Class 9 | Chapter 7 | Example 5 Explanation | NCERT| Congruent Triangles

Class 9 | Chapter 7 | Example 6 Explanation | NCERT| Congruent Triangles

Class 9 | Chapter 7 | Exercise 7.2, Question 1 Proof | NCERT| Congruent Triangles

Class 9 | Chapter 7 | Exercise 7.2, Question 2 Proof | NCERT| Congruent Triangles

Class 9 | Chapter 7 | Exercise 7.2, Question 3 Proof | NCERT| Congruent Triangles

Class 9 | Chapter 7 | Exercise 7.2, Question 4 Proof | NCERT| Congruent Triangles

Class 9 | Chapter 7 | Exercise 7.2, Question 5 Proof | NCERT| Congruent Triangles

Class 9 | Chapter 7 | Exercise 7.2, Question 6 Proof | NCERT| Congruent Triangles

Class 9 | Chapter 7 | Exercise 7.2, Question 7 Proof | NCERT| Congruent Triangles

Class 9 | Chapter 7 | Exercise 7.2, Question 8 Proof | NCERT| Congruent Triangles

Class 9 | Chapter 7 | Theorem 7.4 Proof of SSS (Side Side Side) Congruence rule | NCERT Maths

Theorem 7.5, Chapter 7, Class 9 – RHS congruence rule | Theorem | Geometric Proof

Class 9 | Chapter 7 | Example 7 Explanation | NCERT| Congruent Triangles

Class 9 | Chapter 7 | Example 8 Explanation | NCERT| Congruent Triangles

Class 9 | Chapter 7 | Exercise 7.3, Question 1 Proof | NCERT| Congruent Triangles

Class 9 | Chapter 7 | Exercise 7.3, Question 2 Proof | NCERT| Congruent Triangles

Class 9 | Chapter 7 | Exercise 7.3, Question 3 Proof | NCERT| Congruent Triangles

Class 9 | Chapter 7 | Exercise 7.3, Question 4 Proof | NCERT| Congruent Triangles

Class 9 | Chapter 7 | Exercise 7.3, Question 5 Proof | NCERT| Congruent Triangles

Class 9 | Chapter 7 | Theorem 7.6 In a triangle, angle opposite to larger side is greater | NCERT

Class 9 | Chapter 7 | Theorem 7.7 In a triangle, side opposite to greater angle is longer | NCERT

Class 9 | Chapter 7 | Theorem 7.8 The sum of any two sides of a triangle is greater than third side

Equal Or Congruent ? Lines and Angles

The post Class 9 | Chapter 7 | All Solutions | Triangles appeared first on Mathemafia.

Class 9 | Chapter 6 | All Solutions | Lines and Angles

Sunil Syal — Thu, 16 Dec 2021 15:33:53 +0000

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.

Watch complete chapter on YouTube

Class 9 | Chapter 6 | Axiom 6.1, 6.2, 6.3, 6.4 | Axioms and Definitions from Lines and Angles

Theorem 6.1 Chapter 6 Class 9 Maths – If two lines intersect, vertically opposite angles are equal

Class 9 | Chapter 6 | Topic 6.2 Basic Terms and Definitions | Complementary and Supplementary angles

Class 9 | Chapter 6 | Topic 6.2 Basic Terms and Definitions | Different types of angles | NCERT

Class 9 | Chapter 6 | Exercise 6.1, Question 1 | Figure 6.13, Finding angles | NCERT

Class 9 | Chapter 6 | Exercise 6.1, Question 2 | Figure 6.14, Finding angles | NCERT

Class 9 | Chapter 6 | Exercise 6.1, Question 3 Proof | Figure 6.15 | NCERT

Class 9 | Chapter 6 | Exercise 6.1, Question 4 Proof | Figure 6.16 | NCERT

Class 9 | Chapter 6 | Exercise 6.1, Question 5 Proof | Figure 6.17 | NCERT

Class 9 | Chapter 6 | Exercise 6.1, Question 6 Solution | NCERT

Transversal Line and the important concepts related to it ( हिंदी / Hinglish)

Theorem 6.2 Chapter 6 Class 9 Maths – Alternate interior angles theorem – Proof

Theorem 6.3 Chapter 6 Class 9 Maths – Converse of alternate interior angles theorem – Proof

Theorem 6.4 Chapter 6 Class 9 – Interior Angles on the same side of transversal are supplementary

Theorem 6.5 Chapter 6 Class 9 Maths – Explanation | NCERT Maths | Lines and Angles

Theorem 6.6 Chapter 6 Class 9 Maths – Lines parallel to same line are parallel to each other | NCERT

🔥 Example 4 Chapter 6 Class 9 🔥 Explanation | NCERT Maths | Lines And Angles 💁👌😍

Class 9 | Chapter 6 | Example 5 Explanation | NCERT Maths | Lines And Angles

🔥🔥 Example 6 Chapter 6 Class 9 🔥🔥 Explanation | NCERT Maths | Lines And Angles

Question 1, Exercise 6.2, Chapter 6, Class 9 | Solution | NCERT | Finding angles | Lines and Angles

Question 2, Exercise 6.2, Chapter 6, Class 9 | Solution | NCERT | Finding angles | Lines and Angles

Question 3, Exercise 6.2, Chapter 6, Class 9 | Solution | NCERT | Finding angles | Lines and Angles

Question 4, Exercise 6.2, Chapter 6, Class 9 | Solution | NCERT | Finding angles | Lines and Angles

Question 5, Exercise 6.2, Chapter 6, Class 9 | Solution | NCERT | Finding angles | Lines and Angles

Equal Or Congruent ? Lines and Angles

Properties of KITE 🪁 🔥 One diagonal bisects the other at 90 degrees #mathemafia #geometry

⚡⚡ Q3, 6.1, Class 9, Maths 🔥 📐 Figure 6.15 ✍️ NCERT 💯 🧠

🚀 ⚡ Example 1, Chapter 6, Class 9 🔥 Lines and Angles| Figure 6.9 | NCERT

The post Class 9 | Chapter 6 | All Solutions | Lines and Angles appeared first on Mathemafia.