Question

write all criterion for congruence of triangles
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Answer 1

$\huge\underline\mathcal\purple{SSS}$

SSS (Side-Side-Side)

If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.

$\huge\underline\mathcal\purple{SAS}$

SAS (Side-Angle-Side)

If any two sides and angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle, then the two triangles are said to be congruent by SAS rule.

$\huge\underline\mathcal\purple{ASA}$

ASA (Angle-Side- Angle)

If any two angles and side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by ASA rule.

$\huge\underline\mathcal\purple{AAS}$

AAS (Angle-Angle-Side)

AAS stands for Angle-angle-side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.

$\huge\underline\mathcal\purple{RHS}$

RHS (Right angle- Hypotenuse-Side)

If the hypotenuse and a side of a right- angled triangle is equivalent to the hypotenuse and a side of the second right- angled triangle, then the two right triangles are said to be congruent by RHS rule.

$\huge\underline\mathfrak\purple{Bts}$

Answer 2

Answer:

SSS (Side-Side-Side)

If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.

SSS-Congruence Of Triangles

In the above-given figure, AB= PQ, QR= BC and AC=PR, hence Δ ABC ≅ Δ PQR.

SAS (Side-Angle-Side)

If any two sides and angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle, then the two triangles are said to be congruent by SAS rule.

SAS-Congruence Of Triangles

In above given figure, sides AB= PQ, AC=PR and angle between AC and AB equal to angle between PR and PQ i.e. ∠A = ∠P. Hence, Δ ABC ≅ Δ PQR.

ASA (Angle-Side- Angle)

If any two angles and side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by ASA rule.

ASA-Congruence Of Triangles

In above given figure, ∠ B = ∠ Q, ∠ C = ∠ R and sides between ∠B and ∠C , ∠Q and ∠ R are equal to each other i.e. BC= QR. Hence, Δ ABC ≅ Δ PQR.

AAS (Angle-Angle-Side)

AAS stands for Angle-angle-side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.

Students sometime may get confused AAS with ASA congruency. But remember that AAS is for non-included side whereas ASA is for included sides of the triangles.

If there are two triangles say ABC and DEF, then as per AAS rule:

∠B = ∠E

∠C = ∠F

AB = DE

Hence,

Δ ABC ≅ Δ DEF

RHS (Right angle- Hypotenuse-Side)

If the hypotenuse and a side of a right- angled triangle is equivalent to the hypotenuse and a side of the second right- angled triangle, then the two right triangles are said to be congruent by RHS rule.

RHS-Congruence Of Triangles

In above figure, hypotenuse XZ = RT and side YZ=ST, hence triangle XYZ ≅ triangle RST.