Question

In the given figure AB ll CD ,EF parallel to CD and angle GED= 126 ,find angle AGE , angle GEF and angle FGE.​

Answer 1

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:

Answer 2

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...