pls answer.
THIS IS FROM THE CHAPTER TRIANGLES (CLASS 9)
Answers
Answer:
Step-by-step explanation:
Please mark as brainliest
Congruence of triangles:
Two ∆’s are congruent if sides and angles of a triangle are equal to the corresponding sides and angles of the other ∆.
In Congruent Triangles corresponding parts are always equal and we write it in short CPCT i e, corresponding parts of Congruent Triangles.
It is necessary to write a correspondence of vertices correctly for writing the congruence of triangles in symbolic form.
Criteria for congruence of triangles:
There are 4 criteria for congruence of triangles.
SAS( side angle side):
Two Triangles are congruent if two sides and the included angle of a triangle are equal to the two sides and included angle of the the other triangle.
----------------------------------------------------------------------------------------------------
First
use, SAS rule to show congruence of triangles and then use CPCT to show ii
& iii parts.
Given:
In quadrilateral ABCD,
AD = BC &
∠DAB = ∠CBA
To Prove:
(i)
ΔABD ≅ ΔBAC
(ii)
BD=AC
(iii)
∠ABD = ∠BAC
Proof:
i)
In ΔABD & ΔBAC,
AB = BA (Common)
∠DAB = ∠CBA (Given)
AD = BC (Given)
Hence,
ΔABD ≅
ΔBAC.
( by SAS congruence rule).
(ii) Since, ΔABD ≅
ΔBAC
Then, BD = AC (
by CPCT)
(iv) Since, ΔABD ≅ ΔBAC
Then , ∠ABD = ∠BAC (by CPCT)
Read more on Brainly.in - https://brainly.in/question/1399021#readmoreCongruence of triangles:
Two ∆’s are congruent if sides and angles of a triangle are equal to the corresponding sides and angles of the other ∆.
In Congruent Triangles corresponding parts are always equal and we write it in short CPCT i e, corresponding parts of Congruent Triangles.
It is necessary to write a correspondence of vertices correctly for writing the congruence of triangles in symbolic form.
Criteria for congruence of triangles:
There are 4 criteria for congruence of triangles.
SAS( side angle side):
Two Triangles are congruent if two sides and the included angle of a triangle are equal to the two sides and included angle of the the other triangle.
----------------------------------------------------------------------------------------------------
First
use, SAS rule to show congruence of triangles and then use CPCT to show ii
& iii parts.
Given:
In quadrilateral ABCD,
AD = BC &
∠DAB = ∠CBA
To Prove:
(i)
ΔABD ≅ ΔBAC
(ii)
BD=AC
(iii)
∠ABD = ∠BAC
Proof:
i)
In ΔABD & ΔBAC,
AB = BA (Common)
∠DAB = ∠CBA (Given)
AD = BC (Given)
Hence,
ΔABD ≅
ΔBAC.
( by SAS congruence rule).
(ii) Since, ΔABD ≅
ΔBAC
Then, BD = AC (
by CPCT)
(iv) Since, ΔABD ≅ ΔBAC
Then , ∠ABD = ∠BAC (by CPCT)
Step-by-step explanation:
hope you like my answer....
