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RD Sharma Class 9 Solutions Chapter 10 - Congruent Triangles (Ex 10.3) Exercise 10.3 - Free PDF

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Last updated date: 17th May 2024
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Free PDF download of RD Sharma Class 9 Solutions Chapter 10 - Congruent Triangles

Download Free PDF of RD Sharma Class 9 Solutions Chapter 10 - Congruent Triangles Exercise 10.3 solved by Expert Mathematics Teachers on Vedantu.com. All Chapter 10 - Congruent Triangles Ex 10.3 Questions with Solutions for RD Sharma  Class 9 Math are available to help you to revise the complete Syllabus and score more marks. Register for online coaching for IIT JEE (Mains & Advanced) and other engineering entrance exams. Vedantu is a platform that provides free NCERT Solutions and other study materials for students. Science Students who are looking for NCERT Solutions for Class 9 Science will also find the Solutions curated by our expert teachers which are really helpful.

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Competitive Exams after 12th Science

Congruence in Triangles

Congruence in two or more triangles depends upon the measurements of the sides and the angles of the triangles. The three sides of a triangle determine the size of the triangle and the three angles of a triangle determine the shape of the triangle. Two triangles are said to be a pair of congruent triangles if either the pairs of their sides or angles are the same. They have the same shape and size. There are many conditions of congruence in triangles. 

What is the Congruence in Triangles?

The two triangles are congruent if the three angles or three sides of one triangle are equal to the corresponding angles and sides of another triangle. Both the triangles need to be of the same size and the same shape to be congruent. Both the triangles under consideration should be superimposed on each other. When we rotate, reflect, or translate a triangle, its position or appearance seems to be slightly different. In such a case, we need to identify the six parts of a given triangle and their corresponding parts in the other given triangle.

The Conditions of Congruence in Triangles

Two of the triangles are said to be congruent if they are of the same size and of the same shape. It is not necessary that all corresponding sides and angles of the two given triangles should be found to determine if the triangles are congruent. Different conditions by which two triangles are found to be congruent to each other are: 

  • SSS Criterion: Side Side Side

  • SAS Criterion: Side Angle Side

  • ASA Criterion: Angle Side Angle

  • AAS Criterion: Angle Angle Side

  • RHS Criterion: Right angle Hypotenuse Side

Properties of Congruent Triangles                                                              

If two triangles are said to be congruent, then each part of the triangle (side or angle) is congruent to the corresponding part of the other triangle. Once we have proved that two triangles are congruent, you can find the angles or sides of one of them from the other. To remember this efficient idea, some may find it helpful to use the acronym CPCTC, which stands for "Corresponding Parts of Congruent Triangles are Congruent". In addition to the sides and the angles, all other properties of the triangle are the same such as area, perimeter, location of centers, circles etc.

FAQs on RD Sharma Class 9 Solutions Chapter 10 - Congruent Triangles (Ex 10.3) Exercise 10.3 - Free PDF

1. What is the SSS Criterion for Congruence of Triangles mentioned in RD Sharma Class 9 Solutions Chapter 10 - Congruent Triangles (Ex 10.3)? 

Under the SSS criterion (full form Side Side Side criterion), it is considered that two triangles are congruent when three sides of a given triangle are equal to the corresponding sides of the other given triangle.

2. What is the SAS Criterion for Congruence of Triangles mentioned in RD Sharma Class 9 Solutions Chapter 10 - Congruent Triangles (Ex 10.3)?

Under the SAS criterion (full form Side Angle Side criterion), it is considered that two triangles are congruent when the two sides and the included angle of one given triangle are equal to the corresponding sides and the included angle of the other given triangle.

3. What is the ASA Criterion for Congruence of Triangles mentioned in RD Sharma Class 9 Solutions Chapter 10 - Congruent Triangles (Ex 10.3)?

Under the ASA criterion (full form Angle Side Angle Criterion), it is considered that two triangles are congruent when any two angles and the included side of a given triangle are equal to the corresponding angles and the included side of the other given triangle.

4. What is the AAS Criterion for Congruence of Triangles mentioned in RD Sharma Class 9 Solutions Chapter 10 - Congruent Triangles (Ex 10.3)? 

Under the AAS Criterion (full form Angle Angle Side criterion), it is considered that two triangles are congruent if any two angles and the non-included side of one given triangle are equal to the corresponding angles and the non-included side of the other given triangle. 

5. What is the RHS Criterion for Congruence of Triangles? 

Under the RHS criterion (full form Right Angle Hypotenuse Side criterion), it is considered that both of the given triangles are congruent if the hypotenuse and one side of one right-angled triangle are equal to the corresponding side and hypotenuse of the other right-angled triangle. Visit Vedantu’s website or app for a detailed explanation of the same.