Question

Write the corresponding components of ∆ABC and ∆PQR to verify the SAS test.​

Answer 1

Answer:

∆ABC ~ ∆PQR(Let ~ this be the Symbol Of Congruent ) And Now We Need To Find all Corresponding Angles

of The Two Triangle And We Need To Also Find All Ratio Of all Corresponding Sides

Now Let's Move For Solution...

\underline{\bold{Solution..}}

Solution..

Now According To Question It's Said That ...

∆ABC ~ ∆PQR

\underline{\bold{Note-}}

Note−

When It's Given That A Triangle Is Congruent With Another Triangle Then

The Corresponding Angles And Sides Would Be also In The Form OF Given Order .

Example-

Let ...

∆EFG ~ ∆XYZ So Here EFG & XYZ Are Congruent Therefore The Corresponding Angles Would Be ..

< EFG & <XYZ ,

<FGE & < YZX

< GEF & <ZXY

Therefore This All Where The Corresponding Angles.. Now It's Corresponding Sides Are ...

EF & XY

FG & YZ

GE & ZX

Hence This All Where The Corresponding Sides And Angles ...

Now In Question It's Given That ∆ABC ~ ∆PQR ...

Therefore It's Corresponding Angles Would Be

<ABC & < PQR ,

<BCA & <QRA,

<CAB & <RPQ

Hence, This All Are The Corresponding Angles Of ∆ ABC & ∆ PQR ..

Now It's Corresponding Sides Are ...

AB & PQ ,

BC & QR,

CA & RP

Now By Theorem oF C.P.C.T Are Equal That Is Corresponding Parts Of Congruent Triangles Are Equal..

Therefore Here

AB = PQ

BC = QR

CA = RP

As This Sides Are Equal So Their Ration Would Be

Answer 2

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SAS (Side-Angle-Side)

If any two sides and the 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.

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 the 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.

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.