Congruence And Similarity Of Triangles : Download Maths Notes For CTET Exam Free PDF_00.1
Latest Teaching jobs   »   Congruence And Similarity Of Triangles :...

Congruence And Similarity Of Triangles : Download Maths Notes For CTET Exam Free PDF

Congruence And Similarity Of Triangles : Download Maths Notes For CTET Exam Free PDF_40.1

Mathematics is an equally important section for CTET, MPTET, KVS & DSSSB Exams and has even more abundant importance in some other exams conducted by central or state govt. Generally, there are questions asked related to basic concepts and Facts of the Congruence And Similarity Of Triangles.

To let you make the most of Mathematics section, we are providing important facts related to the Congruence And Similarity Of Triangles. At least 2-3 questions are asked from this topic in most of the teaching exams. We wish you all the best of luck to come over the fear of the Mathematics section.

How to Overcome Exam Fever, Especially When You Fear Maths

Congruence and Similarity of Triangles

 

Congruent Triangles: Triangles are congruent when they have exactly the same three sides and exactly the same three angles.

What is “Congruent”?

It means that one shape can become another using turns, flips and/or sliders.

The equal sides and angles may not be in the same position (if there is a turn or a flip), but they are there.

Same Sides: When the sides are same then the triangles are congruent.

For example:

Congruence And Similarity Of Triangles : Download Maths Notes For CTET Exam Free PDF_50.1

Same Angles: Two triangles with the same angles might be congruent.

Congruence And Similarity Of Triangles : Download Maths Notes For CTET Exam Free PDF_60.1

  1. SSS congruent

Side – Side – Side congruence. When two triangles have corresponding sides equal that are congruent as shows below, the triangles are congruent.

Congruence And Similarity Of Triangles : Download Maths Notes For CTET Exam Free PDF_70.1

  1. SAS Congruence

Side – Angle – Side Congruence. When two triangles have corresponding angles and sides equal that are congruent as shown below, the triangles are congruent.

Congruence And Similarity Of Triangles : Download Maths Notes For CTET Exam Free PDF_80.1

  1. ASA Congruence

Angle – Side – Angle Congruence. When two triangles have corresponding angles and sides equal that are congruent as shown below, the triangles themselves are congruent.

Congruence And Similarity Of Triangles : Download Maths Notes For CTET Exam Free PDF_90.1

Mathematics Study Notes For All Teaching Exams

  1. AAS Congruence OR SAA Congruence

Angle – Angle – Side congruence. When two triangles have corresponding angles and sides equal that are congruent as shown below, the triangles are congruent.

Congruence And Similarity Of Triangles : Download Maths Notes For CTET Exam Free PDF_100.1

  1. HL Congruence

Hypotenuse – leg congruence. When two triangles have corresponding sides equal that are congruent as shown below, the triangles are congruent.

Congruence And Similarity Of Triangles : Download Maths Notes For CTET Exam Free PDF_110.1

 

Similarity of Triangles

 

Two triangles are similar if and only if the corresponding sides are in proportion and the corresponding angles are congruent.

How To Score 25+ Marks In Mathematics For CTET Exam?

Methods of proving triangles similar:

  • If two angles of one triangle are congruent to two angles of another triangle, the triangles are similar.

Congruence And Similarity Of Triangles : Download Maths Notes For CTET Exam Free PDF_120.1

If ∠ A = ∠ D

∠ B = ∠ E

Then : ∆ ABC ∼ ∆ DEF

  • If the three sets of corresponding sides of two triangle are in proportion, the triangles are similar.

Congruence And Similarity Of Triangles : Download Maths Notes For CTET Exam Free PDF_130.1

Congruence And Similarity Of Triangles : Download Maths Notes For CTET Exam Free PDF_140.1

Then : ∆ ABC ∼ ∆ DEF

Practice More Mathematics  Quiz Here

  • If an angle of one triangle is congruent to the corresponding angle of another triangle and the lengths of the sides including these angles are in proportion, the triangles are similar.

Congruence And Similarity Of Triangles : Download Maths Notes For CTET Exam Free PDF_150.1

If  ∠ A = ∠ D

Congruence And Similarity Of Triangles : Download Maths Notes For CTET Exam Free PDF_160.1

Then : ∆ ABC ∼ ∆ DEF

  • If a line is parallel to one side of a triangle and intersects the other two sides of the triangle, the line divides these two sides proportionally.

Congruence And Similarity Of Triangles : Download Maths Notes For CTET Exam Free PDF_170.1

Properties of Similar triangles

 

If the two triangles are similar, then for the proportional / corresponding sides have the following results.

Congruence And Similarity Of Triangles : Download Maths Notes For CTET Exam Free PDF_180.1

Congruence And Similarity Of Triangles : Download Maths Notes For CTET Exam Free PDF_190.1

= Ratio of medians

= Ratio of angles bisectors

= Ratio of inradii

= Ratio of circumradii

  1. Ratio of areas = Ratio of squares of corresponding sides.

i.e. If ∆ ABC ∼ ∆ PQR,

Then,

Congruence And Similarity Of Triangles : Download Maths Notes For CTET Exam Free PDF_200.1

  1. In a right-angled triangle, the triangles on each side of the altitude drawn from the vertex of the right angle to the hypotenuse are similar to the original triangle and to each other too.

Congruence And Similarity Of Triangles : Download Maths Notes For CTET Exam Free PDF_210.1

i.e., ∆ ABC ∼ ∆ BDC ∼∆ CDA.

Some facts on Right angle triangle

 

  • CD² = BD × DA
  • BC × CA = BA × CD
  • BC² = BD × BA
  • AC² = AD × BA

Congruence And Similarity Of Triangles : Download Maths Notes For CTET Exam Free PDF_220.1

Area Based question when two triangles are similar

Congruence And Similarity Of Triangles : Download Maths Notes For CTET Exam Free PDF_230.1

If ∆ ABC ∼ ∆ DEF Then

The Ratio of their area is the square of their sides, Medians, Altitudes, Perimeters, Angle Bisectors.

Congruence And Similarity Of Triangles : Download Maths Notes For CTET Exam Free PDF_240.1

Download Mathematics PDF Notes(English)

Download Mathematics PDF Notes (Hindi)

Sharing is caring!

×

Download success!

Thanks for downloading the guide. For similar guides, free study material, quizzes, videos and job alerts you can download the Adda247 app from play store.

Thank You, Your details have been submitted we will get back to you.

Was this page helpful?

Join India's largest learning destination

What You Will get ?

  • Job Alerts
  • Daily Quizzes
  • Subject-Wise Quizzes
  • Current Affairs
  • Previous year question papers
  • Doubt Solving session

Login

OR

Forgot Password?

Join India's largest learning destination

What You Will get ?

  • Job Alerts
  • Daily Quizzes
  • Subject-Wise Quizzes
  • Current Affairs
  • Previous year question papers
  • Doubt Solving session

Sign Up

OR
Join India's largest learning destination

What You Will get ?

  • Job Alerts
  • Daily Quizzes
  • Subject-Wise Quizzes
  • Current Affairs
  • Previous year question papers
  • Doubt Solving session

Forgot Password

Enter the email address associated with your account, and we'll email you an OTP to verify it's you.


Join India's largest learning destination

What You Will get ?

  • Job Alerts
  • Daily Quizzes
  • Subject-Wise Quizzes
  • Current Affairs
  • Previous year question papers
  • Doubt Solving session

Enter OTP

Please enter the OTP sent to
/6


Did not recive OTP?

Resend in 60s

Join India's largest learning destination

What You Will get ?

  • Job Alerts
  • Daily Quizzes
  • Subject-Wise Quizzes
  • Current Affairs
  • Previous year question papers
  • Doubt Solving session

Change Password



Join India's largest learning destination

What You Will get ?

  • Job Alerts
  • Daily Quizzes
  • Subject-Wise Quizzes
  • Current Affairs
  • Previous year question papers
  • Doubt Solving session

Almost there

Please enter your phone no. to proceed
+91

Join India's largest learning destination

What You Will get ?

  • Job Alerts
  • Daily Quizzes
  • Subject-Wise Quizzes
  • Current Affairs
  • Previous year question papers
  • Doubt Solving session

Enter OTP

Please enter the OTP sent to Edit Number


Did not recive OTP?

Resend 60

By skipping this step you will not recieve any free content avalaible on adda247, also you will miss onto notification and job alerts

Are you sure you want to skip this step?

By skipping this step you will not recieve any free content avalaible on adda247, also you will miss onto notification and job alerts

Are you sure you want to skip this step?