In the given figure AB ll CD ,EF parallel to CD and angle GED= 126 ,find angle AGE , angle GEF and angle FGE.
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:
Alternate angles:When two lines are crossed by another line the pair of angles on opposite sides of the transversal is called alternate angles.
Theorem 1:If a transversal intersects two Parallel Lines then each pair of alternate interior angles is equal.
Theorem 2 :If a transversal intersects two lines such that a pair alternate interior angle is equal then the two lines are parallel.
SOLUTION:
Given: ∠AGE=126°
∠AGE=∠GED=126∘ [alternate interior angles]
(ii) ∠GED=∠GEF+∠FED=126∘
∠GEF + 90° =126°
(GIVEN that EF⊥CD)
∠GEF=126°−90°=36°
∠GEF=36°
(iii) ∠CEG+∠GED=180°
(GIVEN ∠GED=126∘)
∠CEG+126° =180°
∠CEG=180° −126°
∠CEG=54°
∠FGE=∠CEG= 54° (alternate angles)
HOPE THIS WILL HELP YOU...