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Byju's Answer

Standard VIII

Mathematics

SSS Postulate

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Question

From the information shown in the figure, state the test assuring the congruence of $△ A B C$ and $△ P Q R$ . Write the remaining congruent parts of the triangles.

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Solution

In $Δ A B C$ and $Δ P Q R$

$A B = P Q (A s g i v e n f i g u r e)$

$B C = P R (A s g i v e n f i g u r e)$

$∠ B A C = ∠ P Q R (R i g h t a n g l e t r i a n g l e)$

Then,

$Δ A B C ≅ Δ P Q R$ $(S . A . S . c o n g r u e n c y)$
Hence, $A C = Q R$ (Remaining part)

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Similar questions

Q. From the information shown in the figure, state the test assuring the congruence of

∆

ABC and

∆

PQR. Write the remaining congruent parts of the triangles.

Q. As shown in the following figure, in

∆

LMN and

∆

PNM, LM = PN, LN = PM. Write the test which assures the congruence of the two triangles. Write their remaining congruent parts.

Observe the information shown in pairs of triangles given below. State the test by which the two triangles are congruent. Write the remaining congruent parts of the triangles.

(i)

From the information shown in the figure,

∆

ABC and

∆

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∠

ABC

≅ ∠

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seg BC

≅

seg QR

∠

ACB

≅

∠

PRQ

∴ ∆

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≅

∆

PQR .......

3243432

test

∴ ∠

BAC

≅

3243432

.......corresponding angles of congruent triangles.

\begin{array}{l} seg AB ≅ 1234 \\ and 1234 ≅ seg PR \end{array}\} . . . corresponding sides of congruent triangles

(ii)

From the information shown in the figure,

∆

PTQ and

∆

STR

seg PT

≅

seg ST

∠

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≅

∠

STR...... vertically opposite angles

∴ ∆

PTQ

≅

∆

STR .......

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test

\begin{array}{l} ∴ ∠ TPQ ≅ 1234 \\ and 1234 ≅ ∠ TRS \end{array}\} . . . corresponding angles of congruent triangles

seg PQ

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corresponding sides of congruent triangles

Q. Observe the information shown in pairs of triangles given below. State the test by which the two triangles are congruent. Write the remaining congruent parts of the triangles.

Q. In the figures given below, some congruent parts are indicated by identical marks.
(1) Write the test of congruence by which the pairs of triangle in each figure is congruent.
(2) Write proper correspondence between the vertices of triangle while writing the names of triangle.
(3) Also write the remaining congruent parts of the congruent triangle.

(i)

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From the information shown in the figure, state the test assuring the congruence of △ABC and △PQR. Write the remaining congruent parts of the triangles.

In ΔABC and ΔPQR AB=PQ(Asgivenfigure) BC=PR(Asgivenfigure) ∠BAC=∠PQR(Rightangletriangle) Then, ΔABC≅ΔPQR (S.A.S.congruency) Hence,AC=QR (Remaining part)

From the information shown in the figure, state the test assuring the congruence of $△ A B C$ and $△ P Q R$ . Write the remaining congruent parts of the triangles.

In $Δ A B C$ and $Δ P Q R$

$A B = P Q (A s g i v e n f i g u r e)$

$B C = P R (A s g i v e n f i g u r e)$

$∠ B A C = ∠ P Q R (R i g h t a n g l e t r i a n g l e)$

Then,

$Δ A B C ≅ Δ P Q R$ $(S . A . S . c o n g r u e n c y)$
Hence, $A C = Q R$ (Remaining part)