Question

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Answer 1

Answer:

1. a

2. b

3. d

4. a

Step-by-step explanation:

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Answer 2

$\large\underline{\sf{Solution-}}$

We know that If

$\rm :\longmapsto\:\triangle \: ABC \: \cong \: \triangle \: DEF$

Then,

$\rm :\longmapsto\:AB = DE$

$\rm :\longmapsto\:BC = EF$

$\rm :\longmapsto\:AC = DF$

and

$\rm :\longmapsto\:\angle \: A \: = \: \angle \: D$

$\rm :\longmapsto\:\angle \: B \: = \: \angle \: E$

$\rm :\longmapsto\:\angle \: C \: = \: \angle \: F$

Let's solve the problem now!!!

$\large\underline{\sf{Solution-41}}$

Given that,

$\rm :\longmapsto\:\triangle \: DBA \: \leftrightarrow \: \triangle \: EFG$

It implies,

$\rm :\longmapsto\:DB \: \leftrightarrow \:EF$

$\rm :\longmapsto\:BA \: \leftrightarrow \:FG$

$\rm :\longmapsto\:DA \: \leftrightarrow \:EG$

$\rm :\longmapsto\:\angle \: D \: \leftrightarrow \:\angle \: E$

$\rm :\longmapsto\:\angle \: B \: \leftrightarrow \:\angle \: F$

$\rm :\longmapsto\:\angle \: A \: \leftrightarrow \:\angle \: G$

Hence,

$\bf\implies \:\angle \: EGF \: \leftrightarrow \: \: \angle \: BAD$

Option (c) is correct

$\large\underline{\sf{Solution-42}}$

In triangle LMN,

The side included between the angles ∠L and ∠M is LM.

Hence,

Option (a) is correct.

$\large\underline{\sf{Solution-43}}$

Given,

$\red{\rm :\longmapsto\:\triangle \: HGF \: \cong \: \triangle \: FJH}$

It implies,

$\rm :\longmapsto\:\angle \: H \: \cong \: \angle \: F$

$\rm :\longmapsto\:\angle \: G \: \cong \: \angle \: J$

$\rm :\longmapsto\:\angle \: F \: \cong \: \angle \: H$

Its true by CPCTC means Corresponding Parts of Congruent Triangle Criterion.

Hence,

Option (b) is correct.

$\large\underline{\sf{Solution-44}}$

We know,

SAS Congruency Rule means two sides and included angle of one triangle must be equal to two sides and included angle of other triangle.

Here,

Given two triangles, ABC and XYZ

Such that,

• AB = XY

• AC = XZ

So, for SAS, we need included angle between AB & AC of triangle ABC and included angle between XY & XZ of triangle XYZ.

$\rm :\longmapsto\:\angle \: A \: = \: \angle \: X$

Hence,

Option (c) is correct.

Additional Information  :

1) AAS Congruency  :

If two angles and one side of one triangle is equal to two angles and one side of a triangle, then they are congruent.

Example :

In ΔABC and ΔDEF, ∠A = ∠D, ∠B = ∠E and BC= EF then ΔABC ≅ ΔDEF by AAS criteria.

2) ASA Congruency  :

If two angles and included side of one triangle are respectively equal to two angles and included side of another triangle, then the two triangles are congruent.

Example :

In ΔABC and ΔDEF, ∠A = ∠D, ∠C = ∠F and AC = DF then ΔABC ≅ ΔDEF by ASA criteria.

3) SSS Congruency :

If the corresponding sides of two triangles are equall, then the two triangles are congruent.

Example :

In ΔXYZ and ΔLMN, XY = LM, YZ = MN and XZ = LN then ΔXYZ ≅ ΔLMN by SSS criteria.

4) SAS Congruency :

If in two triangles, one pair of corresponding sides are equall and the included angles are equal then the two triangles are congruent.

Example :

In ∆ABC & ∆DEF,∠A = ∠D, AB = DE, AC = DF then ∆ABC ≅ ∆DEF by SAS criteria.

5) RHS Congruency

If in two triangles, right angle, Hypotenuse and one side are equal, then triangles are congruent.

Example :

In ∆ABC & ∆DEF,∠A = ∠D = 90°, AB = DE, BC = EF then ∆ABC ≅ ∆DEF by RHS criteria.