Class 7 Exam > Class 7 Questions > ∆ABC is an isoscelesangle in which AB=BC.this...
Start Learning for Free
∆ABC is an isoscelesangle in which AB=BC.this triangle is congruent to ∆PQR.if AB=6cm,QR=10cm, find perimeter of ∆ABC
?
Most Upvoted Answer
∆ABC is an isoscelesangle in which AB=BC.this triangle is congruent to...
If the triangles are congruent then AB=PQ=BC=QR because they are isosceles triangles so PR is also equal to AC. according to SSS congruency. then we find AB=6,BC=6,AC=10.
Perimeter of the triangle=sum of all sides
=6+6+10=22cm. it is your answer.
Perimeter of the triangle=sum of all sides
=6+6+10=22cm. it is your answer.
Community Answer
∆ABC is an isoscelesangle in which AB=BC.this triangle is congruent to...
Given:
- Triangle ABC is an isosceles triangle with AB=BC.
- Triangle ABC is congruent to triangle PQR.
- AB = 6 cm and QR = 10 cm.
To Find:
The perimeter of triangle ABC.
Solution:
To find the perimeter of triangle ABC, we need to find the lengths of sides AB, BC, and AC.
Step 1: Understanding Congruence of Triangles
Congruence of triangles means that two triangles are identical in shape and size. If two triangles are congruent, it means that their corresponding sides and angles are equal.
Step 2: Properties of an Isosceles Triangle
In an isosceles triangle, the two legs (sides opposite to the equal angles) are equal. In triangle ABC, AB = BC.
Step 3: Congruence of Triangles
Triangle ABC is congruent to triangle PQR. This means that the corresponding sides and angles of both triangles are equal.
Step 4: Applying Congruence to Find the Missing Side
Since AB = BC in triangle ABC, it means that QR = RP in triangle PQR. Therefore, RP = 6 cm.
Step 5: Finding the Length of AC
To find the length of AC, we can use the fact that the sum of the lengths of the two congruent sides of an isosceles triangle is greater than the third side.
In triangle ABC, AB = BC = 6 cm. Therefore, AC < 6="" cm="" +="" 6="" cm="12" />
Step 6: Finding the Perimeter
Now that we know the lengths of sides AB, BC, and AC, we can find the perimeter of triangle ABC by summing up the lengths of all three sides.
Perimeter of triangle ABC = AB + BC + AC = 6 cm + 6 cm + AC
Step 7: Final Calculation
To find the perimeter, we need to determine the length of AC.
Since AC < 12="" cm,="" and="" the="" length="" of="" qr="" is="" given="" as="" 10="" cm,="" ac="" must="" be="" less="" than="" 10="" />
Therefore, the perimeter of triangle ABC is 6 cm + 6 cm + AC.
Conclusion:
The perimeter of triangle ABC is 12 cm + AC, where AC is less than 10 cm (as AC < 12="" cm="" and="" qr="10" cm).="" 12="" cm="" and="" qr="10" />
- Triangle ABC is an isosceles triangle with AB=BC.
- Triangle ABC is congruent to triangle PQR.
- AB = 6 cm and QR = 10 cm.
To Find:
The perimeter of triangle ABC.
Solution:
To find the perimeter of triangle ABC, we need to find the lengths of sides AB, BC, and AC.
Step 1: Understanding Congruence of Triangles
Congruence of triangles means that two triangles are identical in shape and size. If two triangles are congruent, it means that their corresponding sides and angles are equal.
Step 2: Properties of an Isosceles Triangle
In an isosceles triangle, the two legs (sides opposite to the equal angles) are equal. In triangle ABC, AB = BC.
Step 3: Congruence of Triangles
Triangle ABC is congruent to triangle PQR. This means that the corresponding sides and angles of both triangles are equal.
Step 4: Applying Congruence to Find the Missing Side
Since AB = BC in triangle ABC, it means that QR = RP in triangle PQR. Therefore, RP = 6 cm.
Step 5: Finding the Length of AC
To find the length of AC, we can use the fact that the sum of the lengths of the two congruent sides of an isosceles triangle is greater than the third side.
In triangle ABC, AB = BC = 6 cm. Therefore, AC < 6="" cm="" +="" 6="" cm="12" />
Step 6: Finding the Perimeter
Now that we know the lengths of sides AB, BC, and AC, we can find the perimeter of triangle ABC by summing up the lengths of all three sides.
Perimeter of triangle ABC = AB + BC + AC = 6 cm + 6 cm + AC
Step 7: Final Calculation
To find the perimeter, we need to determine the length of AC.
Since AC < 12="" cm,="" and="" the="" length="" of="" qr="" is="" given="" as="" 10="" cm,="" ac="" must="" be="" less="" than="" 10="" />
Therefore, the perimeter of triangle ABC is 6 cm + 6 cm + AC.
Conclusion:
The perimeter of triangle ABC is 12 cm + AC, where AC is less than 10 cm (as AC < 12="" cm="" and="" qr="10" cm).="" 12="" cm="" and="" qr="10" />
Attention Class 7 Students!
To make sure you are not studying endlessly, EduRev has designed Class 7 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 7.
|
Explore Courses for Class 7 exam
|
|
Similar Class 7 Doubts
Top Courses for Class 7View all
∆ABC is an isoscelesangle in which AB=BC.this triangle is congruent to ∆PQR.if AB=6cm,QR=10cm, find perimeter of ∆ABC Related: NCERT Solutions - Congruence of Triangles?
Question Description
∆ABC is an isoscelesangle in which AB=BC.this triangle is congruent to ∆PQR.if AB=6cm,QR=10cm, find perimeter of ∆ABC Related: NCERT Solutions - Congruence of Triangles? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about ∆ABC is an isoscelesangle in which AB=BC.this triangle is congruent to ∆PQR.if AB=6cm,QR=10cm, find perimeter of ∆ABC Related: NCERT Solutions - Congruence of Triangles? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ∆ABC is an isoscelesangle in which AB=BC.this triangle is congruent to ∆PQR.if AB=6cm,QR=10cm, find perimeter of ∆ABC Related: NCERT Solutions - Congruence of Triangles?.
∆ABC is an isoscelesangle in which AB=BC.this triangle is congruent to ∆PQR.if AB=6cm,QR=10cm, find perimeter of ∆ABC Related: NCERT Solutions - Congruence of Triangles? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about ∆ABC is an isoscelesangle in which AB=BC.this triangle is congruent to ∆PQR.if AB=6cm,QR=10cm, find perimeter of ∆ABC Related: NCERT Solutions - Congruence of Triangles? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ∆ABC is an isoscelesangle in which AB=BC.this triangle is congruent to ∆PQR.if AB=6cm,QR=10cm, find perimeter of ∆ABC Related: NCERT Solutions - Congruence of Triangles?.
Solutions for ∆ABC is an isoscelesangle in which AB=BC.this triangle is congruent to ∆PQR.if AB=6cm,QR=10cm, find perimeter of ∆ABC Related: NCERT Solutions - Congruence of Triangles? in English & in Hindi are available as part of our courses for Class 7.
Download more important topics, notes, lectures and mock test series for Class 7 Exam by signing up for free.
Here you can find the meaning of ∆ABC is an isoscelesangle in which AB=BC.this triangle is congruent to ∆PQR.if AB=6cm,QR=10cm, find perimeter of ∆ABC Related: NCERT Solutions - Congruence of Triangles? defined & explained in the simplest way possible. Besides giving the explanation of
∆ABC is an isoscelesangle in which AB=BC.this triangle is congruent to ∆PQR.if AB=6cm,QR=10cm, find perimeter of ∆ABC Related: NCERT Solutions - Congruence of Triangles?, a detailed solution for ∆ABC is an isoscelesangle in which AB=BC.this triangle is congruent to ∆PQR.if AB=6cm,QR=10cm, find perimeter of ∆ABC Related: NCERT Solutions - Congruence of Triangles? has been provided alongside types of ∆ABC is an isoscelesangle in which AB=BC.this triangle is congruent to ∆PQR.if AB=6cm,QR=10cm, find perimeter of ∆ABC Related: NCERT Solutions - Congruence of Triangles? theory, EduRev gives you an
ample number of questions to practice ∆ABC is an isoscelesangle in which AB=BC.this triangle is congruent to ∆PQR.if AB=6cm,QR=10cm, find perimeter of ∆ABC Related: NCERT Solutions - Congruence of Triangles? tests, examples and also practice Class 7 tests.
|
|
Explore Courses for Class 7 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup