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Properties of Isosceles and Equilateral Triangles

Which congrue...

Question

Which congruence criterion do you use in the following?
Given: RP $=$ ZX, RQ $=$ ZY, $∠$ PRQ $= ∠$ XZY. So $Δ$ PQR $≅ Δ$ XYZ.

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Solution

By SAS congruence criterion,
since it is given that
$R P$ = $Z X$ , $R Q$ = $Z Y$ and $∠$ PRQ $= ∠$ XZY.
The two sides and one angle in one of the triangle are equal to the corresponding sides and the angle of
other triangle.
Therefore,
$Δ$ PQR $≅ Δ$ XYZ.

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Similar questions

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

∠ P R Q = ∠ X Z Y

So, △ P Q R ≅ △ X Y Z

Question 1 (b)\angle{F}
Which congruence criterion do you use in the following?

Given: RP = ZX, RQ = ZY, $∠ P R Q = ∠ X Z Y$
So, $Δ P Q R ≅ Δ X Y$

∠ P R Q = ∠ X Z Y

Δ P Q R ≅ Δ X Y Z

Question 1 (b)
Which congruence criterion do you use in the following?
Given: RP = ZX, RQ = ZY, $Δ P R Q = Δ X Z Y$
So $Δ P Q R = Δ X Y$

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