Construct the following quadrilateral ABCD with the following information ab is equal to 8 cm BC is equal to 5.6 CM CD is equal to 7.2 CM angle b is equal to 45 degree angle C is equal to 90 degree.
Answers
Answer:
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.
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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)
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Hope this will help you.....
Step-by-step explanation: