Class 9 - Triangles Archives – Mathemafia http://sh016.global.temp.domains/~mathemaf/category/class-9-triangles/ 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 Class 9 - Triangles Archives – Mathemafia http://sh016.global.temp.domains/~mathemaf/category/class-9-triangles/ 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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]]> Class 9 | Chapter 7 | All Solutions | Triangles https://mathemafia.com/class-9-chapter-07-all-solutions-triangles/ Thu, 16 Dec 2021 15:34:06 +0000 http://sh016.global.temp.domains/~mathemaf/?p=7186 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

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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.Β 

Watch complete chapter on YouTube

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]]> Class 9 | Chapter 7 | Triangles | Example 9 https://mathemafia.com/class-9-chapter-7-triangles-example-9/ Wed, 16 Sep 2020 02:53:52 +0000 http://sh016.global.temp.domains/~mathemaf/?p=1994 Example 9: D is a point on side BC of βˆ† ABC such that AD = AC (see Fig. 7.47). Show that AB > AD. Example 8 Class 9 | Home

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Example 9: D is a point on side BC of βˆ† ABC such that AD = AC (see Fig. 7.47). Show that AB > AD.

Example 8
Class 9 | Home

Chapter 7 – Triangles

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.Β 

Watch complete chapter on YouTube
​

Theorems

Theorem 7.1

Theorem 7.2

Theorem 7.3

Theorem 7.4

Theorem 7.5

Theorem 7.6

Theorem 7.7

Theorem 7.8

Exercise 7.1

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Exercise 7.2

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Exercise 7.3

Question 1

Question 2

Question 3

Question 4

Question 5

Exercise 7.4

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

Example 9

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]]> Class 9 | Chapter 7 | Triangles | Example 8 https://mathemafia.com/class-9-chapter-7-triangles-example-8/ Wed, 16 Sep 2020 02:53:48 +0000 http://sh016.global.temp.domains/~mathemaf/?p=1993 Example 8: P is a point equidistant from two lines l and m intersecting at point A (see Fig. 7.38). Show that the line AP bisects the angle between them. Example 7 Example 9

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Example 8: P is a point equidistant from two lines l and m intersecting at point A (see Fig. 7.38). Show that the line AP bisects the angle between them.

Example 7
Example 9

Chapter 7 – Triangles

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.Β 

Watch complete chapter on YouTube
​

Theorems

Theorem 7.1

Theorem 7.2

Theorem 7.3

Theorem 7.4

Theorem 7.5

Theorem 7.6

Theorem 7.7

Theorem 7.8

Exercise 7.1

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Exercise 7.2

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Exercise 7.3

Question 1

Question 2

Question 3

Question 4

Question 5

Exercise 7.4

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

Example 9

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]]> Class 9 | Chapter 7 | Triangles | Example 7 https://mathemafia.com/class-9-chapter-7-triangles-example-7/ Wed, 16 Sep 2020 02:53:43 +0000 http://sh016.global.temp.domains/~mathemaf/?p=1992 Example 7: AB is a line-segment. P and Q are points on opposite sides of AB such that each of them is equidistant from the points A and B (see Fig. 7.37). Show that the line PQ is the perpendicular…

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Example 7: AB is a line-segment. P and Q are points on opposite sides of AB such that each of them is equidistant from the points A and B (see Fig. 7.37). Show that the line PQ is the perpendicular bisector of AB.

Example 6
Example 8

Chapter 7 – Triangles

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.Β 

Watch complete chapter on YouTube
​

Theorems

Theorem 7.1

Theorem 7.2

Theorem 7.3

Theorem 7.4

Theorem 7.5

Theorem 7.6

Theorem 7.7

Theorem 7.8

Exercise 7.1

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Exercise 7.2

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Exercise 7.3

Question 1

Question 2

Question 3

Question 4

Question 5

Exercise 7.4

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

Example 9

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]]> Class 9 | Chapter 7 | Triangles | Example 6 https://mathemafia.com/class-9-chapter-7-triangles-example-6/ Wed, 16 Sep 2020 02:53:39 +0000 http://sh016.global.temp.domains/~mathemaf/?p=1991 Example 6: In an isosceles triangle ABC with AB = AC, D and E are points on BC such that BE = CD (see Fig. 7.29). Show that AD = AE. Example 5 Example 7

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Example 6: In an isosceles triangle ABC with AB = AC, D and E are points on BC such that BE = CD (see Fig. 7.29). Show that AD = AE.

Example 5
Example 7

Chapter 7 – Triangles

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.Β 

Watch complete chapter on YouTube
​

Theorems

Theorem 7.1

Theorem 7.2

Theorem 7.3

Theorem 7.4

Theorem 7.5

Theorem 7.6

Theorem 7.7

Theorem 7.8

Exercise 7.1

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Exercise 7.2

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Exercise 7.3

Question 1

Question 2

Question 3

Question 4

Question 5

Exercise 7.4

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

Example 9

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]]> Class 9 | Chapter 7 | Triangles | Example 5 https://mathemafia.com/class-9-chapter-7-triangles-example-5/ Wed, 16 Sep 2020 02:53:34 +0000 http://sh016.global.temp.domains/~mathemaf/?p=1990 Example 5: E and F are respectively the mid-points of equal sides AB and AC of βˆ† ABC (see Fig. 7.28). Show that BF = CE. Example 4 Example 6

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Example 5: E and F are respectively the mid-points of equal sides AB and AC of βˆ† ABC (see Fig. 7.28). Show that BF = CE.

Example 4
Example 6

Chapter 7 – Triangles

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.Β 

Watch complete chapter on YouTube
​

Theorems

Theorem 7.1

Theorem 7.2

Theorem 7.3

Theorem 7.4

Theorem 7.5

Theorem 7.6

Theorem 7.7

Theorem 7.8

Exercise 7.1

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Exercise 7.2

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Exercise 7.3

Question 1

Question 2

Question 3

Question 4

Question 5

Exercise 7.4

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

Example 9

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]]> Class 9 | Chapter 7 | Triangles | Example 4 https://mathemafia.com/class-9-chapter-7-triangles-example-4/ Wed, 16 Sep 2020 02:53:28 +0000 http://sh016.global.temp.domains/~mathemaf/?p=1989 Example 4: In βˆ† ABC, the bisector AD of ∠ A is perpendicular to side BC (see Fig. 7.27). Show that AB = AC and βˆ† ABC is isosceles. Example 3 Example 5

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Example 4: In βˆ† ABC, the bisector AD of ∠ A is perpendicular to side BC (see Fig. 7.27). Show that AB = AC and βˆ† ABC is isosceles.

Example 3
Example 5

Chapter 7 – Triangles

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.Β 

Watch complete chapter on YouTube
​

Theorems

Theorem 7.1

Theorem 7.2

Theorem 7.3

Theorem 7.4

Theorem 7.5

Theorem 7.6

Theorem 7.7

Theorem 7.8

Exercise 7.1

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Exercise 7.2

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Exercise 7.3

Question 1

Question 2

Question 3

Question 4

Question 5

Exercise 7.4

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

Example 9

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]]> Class 9 | Chapter 7 | Triangles | Example 3 https://mathemafia.com/class-9-chapter-7-triangles-example-3/ Wed, 16 Sep 2020 02:53:24 +0000 http://sh016.global.temp.domains/~mathemaf/?p=1988 Example 3: Line-segment AB is parallel to another line-segment CD. O is the mid-point of AD (see Fig. 7.15). Show that (i) βˆ†AOB β‰… βˆ†DOC (ii) O is also the mid-point of BC. Example 2 Example 4

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Example 3: Line-segment AB is parallel to another line-segment CD. O is the mid-point of AD (see Fig. 7.15). Show that (i) βˆ†AOB β‰… βˆ†DOC (ii) O is also the mid-point of BC.

Example 2
Example 4

Chapter 7 – Triangles

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.Β 

Watch complete chapter on YouTube
​

Theorems

Theorem 7.1

Theorem 7.2

Theorem 7.3

Theorem 7.4

Theorem 7.5

Theorem 7.6

Theorem 7.7

Theorem 7.8

Exercise 7.1

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Exercise 7.2

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Exercise 7.3

Question 1

Question 2

Question 3

Question 4

Question 5

Exercise 7.4

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

Example 9

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]]> Class 9 | Chapter 7 | Triangles | Example 2 | Perpendicular bisector theorem https://mathemafia.com/class-9-chapter-7-triangles-example-2/ Wed, 16 Sep 2020 02:53:20 +0000 http://sh016.global.temp.domains/~mathemaf/?p=1987 Example 2: AB is a line segment and line l is its perpendicular bisector. If a point P lies on l, show that P is equidistant from A and B. Example 1 Example 3

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Example 2: AB is a line segment and line l is its perpendicular bisector. If a point P lies on l, show that P is equidistant from A and B.

Example 1
Example 3

Chapter 7 – Triangles

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.Β 

Watch complete chapter on YouTube
​

Theorems

Theorem 7.1

Theorem 7.2

Theorem 7.3

Theorem 7.4

Theorem 7.5

Theorem 7.6

Theorem 7.7

Theorem 7.8

Exercise 7.1

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Exercise 7.2

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Exercise 7.3

Question 1

Question 2

Question 3

Question 4

Question 5

Exercise 7.4

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

Example 9

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