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SAS Congruency Postulate

Which congrue...

Question

Which congruence criterion is used in the following?
Given: $∠ M L N = ∠ F G H, ∠ N M L = ∠ H F G, M L = F G$
So $Δ L M N ≅ Δ G F H$ [2 MARKS]

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Solution

Steps: 1 Mark
Proof: 1 Mark

It is given that,

$∠ M L N = ∠ F G H$ ,

$∠ N M L = ∠ H F G$ ,

$M L = F G .$

$\Rightarrow$ The two angles and an included side of one triangle are equal to the corresponding angles and an included side of other triangles.

$∴ Δ L M N ≅ Δ G F H$ [By ASA congruence criterion]

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Similar questions

∠ M L N = ∠ F G H, ∠ N M L = ∠ H F G, M L = F G

Δ L M N ≅ Δ G F H

Which congruence criterion is used in the following?

Given: $∠ M L N = ∠ F G H, ∠ N M L = ∠ H F G, M L = F G$
So, $Δ L M N ≅ Δ G F H$

Which congruence criterion do you use in the following?

(a) Given: AC = DF

AB = DE

BC = EF

So, ΔABC ≅ ΔDEF

(b) Given: ZX = RP

RQ = ZY

∠PRQ = ∠XZY

So, ΔPQR ≅ ΔXYZ

∠NML = ∠GFH

ML = FG

So, ΔLMN ≅ ΔGFH

(d) Given: EB = DB

AE = BC

∠A = ∠C = 90°

So, ΔABE ≅ ΔCDB

Which congruence criterion is used in the following:

Given: $∠$ MLN = $∠$ FGH , $∠$ NML= $∠$ HFG and LM = HF. So $△$ LMN ≅ $△$ GFH.

∠ NML = ∠ GFH

ML = FG

So, ΔLMN ≅ ΔGFH

(ii) Given: EB = DB

AE = BC

∠ A = ∠ C = 90°

So, ΔABE ≅ ΔCDB
.
[4 MARKS]

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