Question

if triangle ABC ~ triangle PQR write the corresponding angles of two Triangles and write the ratios of corresponding sides

Answer 1

$\underline{\bold{Hey\:Mate\:Here\:Is\:Your\:Answer\:}}$

$\underline{\bold{Given\:That....}}$

∆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...

$\underline{\bold{Solution..}}$

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

∆ABC ~ ∆PQR

$\underline{\bold{Note-}}$ 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

$\boxed{\bold{ 1\: : \: 1 }}$

$\boxed{\boxed{\bold{Thanks}}}$

Answer 2

The corresponding angles of two triangles and the ratios of corresponding sides can be written as follows.  

According to the question, the triangles ABC and PQR are similar. When two triangles are similar, their corresponding angles are the same. Hence, the corresponding angles can be written as follows.

$\angle A = \angle P$  

$\angle B = \angle Q$  

$\angle C = \angle R$

In similar triangles, the corresponding sides are in proportion with each other. So, the corresponding sides of the two triangles are written as follows.

$\frac{AB}{PQ} = \frac{BC}{QR} = \frac{AC}{PR}$